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Gas-liquid mass transfer rates by gas pumping : agitators in oxygen pressure leaching systems Dawson-Amoah, James 1991

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GAS-LIQUID MASS TRANSFER RATES BY GAS PUMPING A G I T A T O R S IN O X Y G E N P R E S S U R E L E A C H I N G S Y S T E M S By James Dawson-Amoah B. Sc. (Hons.) Metallurgical Eng., University of Science & Technology, Kumasi, Ghana, 1986 A THESIS SUBMITTED IN P A R T I A L F U L F I L L M E N T OF THE REQUIREMENTS FOR THE DEGREE OF M A S T E R OF APPLIED SCIENCE in THE F A C U L T Y OF G R A D U A T E STUDIES (Department of Metals and Materials Engineering) We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH C O L U M B I A March 1991 © James Dawson-Amoah, 1991 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of H£T?rLS'4/flA&TE£'A-i-S ^ A J 6-The University of British Columbia Vancouver, Canada Date ' S ^ Afit.iL [ <=\<\ , DE-6 (2/88) ii Abstract Recent developments have indicated high oxygen consumption rates of about 35 g-mole/m3-rnin during oxidative pressure leaching. At such high oxygen consumption rates the mass transfer of dissolved oxygen at the gas-liquid interface may become rate-hmiting. The objective of this study was to obtain an understanding of the gas-liquid mass transfer processes that take place in mechanically agitated pressure leaching systems. The classical reaction between sodium sulphite and dissolved oxygen to form sulphate at atmospheric pressure was used to determine the oxygen mass transfer rates in a 200-liter asyrnmetrical plastic tank, modelled after the shape of the first compartment of the zinc pressure leach. The effect of this asymmetry was compared with the work of Swiniarski who used a cylindrical syrnmetrical tank of similar volume. A number of process variables such as the impeller type and size, the impeller speed, the impeller immersion depth and the effect of full baffles that affect mixing were investigated. Also, the volumetric power consumption associated with the mass transfer rates were measured. The results indicate that the asymmetrical tank is at least 3.6 times more efficient in mass transfer than the symmetrical tank. There is a critical speed below which the mass transfer parameter, Kg, is almost zero and above which Kg increases almost linearly with impeller tip speed. A simple energy balance model for bubble creation can predict the critical tip speed. It is shown that Kg is enhanced at shallow depths, with a corresponding high mass transfer to energy ratio. The relative effectiveness of impeller types and sizes with regard to the use of power for gas-liquid mass transfer was established. Full baffles degrade the mass transfer rate at increased depth of impeller immersion. iii The results also add substantial support to the findings provided by DeGraaf [5] that: (i) The dimensionless correlations used in liquid mixing systems do not accurately predict dispersion rates by agitators, (ii) The optimum conditions for gas dispersion and the consequent generation of gas-liquid interfacial area are different from fluid mixing, (iii) The classical mixing power equations for impellers markedly overestimate power requirements during impeller gas dispersion. iv Table of Contents Abstract ii Table of Contents iv List of Figures , vii List of Tables x List of Symbols xi Acknowledgements xiv CHAPTER 1 INTRODUCTION 1 1.1 Oxygen Pressure Leaching Technology 1 1.2 Concept of Oxygen Utilization in Oxidative Pressure Leaching Processes 3 CHAPTER 2 LITERATURE REVIEW 13 2.1 Mass Transfer in Gas-Liquid Systems 13 2.1.1 Physical absorption 13 2.1.2 Mass transfer with chemical reaction 15 2.1.3 Gas-liquid interfacial area 18 2.2 Liquid Mixing and Agitation 20 2.2.1 Basic reactors 21 2.2.2 Impeller types 22 2.2.3 Tank baffles 24 2.2.4 Impeller location and proximity 25 2.3 Gas Pumping and Dispersion by Agitators 26 2.4 Impeller Power Requirement 28 2.4.1 Power correlations 33 V 2.4.2 Power reductions through gas sparging and entrainment of gas 33 2.4.3 Power measurement 34 2.5 Overview of Past Work on Oxygen Mass Transfer 35 2.5.1 Sodium sulphite oxidation 35 2.5.2 Recent studies on oxygen mass transfer 39 C H A P T E R 3 E X P E R I M E N T A L 42 3.1 Apparatus 42 3.2 Experimental procedure 45 C H A P T E R 4 R E S U L T S A N D D I S C U S S I O N 49 4.1 Experimental Results 49 4.1.1 Unbaffled Tank Systems 49 4.1.1.1 Varying speed at constant impeller depth 49 4.1.1.2 Effect of depth of impeller immersion 55 4.1.2 Baffled Tank Systems 64 4.1.2.1 Effect of Impeller Type 64 4.1.2.2 Effect of ImpeUer Depth 64 4.1.2.3 Effect of Diameter 68 4.1.3 Comparison of Baffled and Unbaffled Tank systems 71 4.1.3.1 Impeller depth at 11.5 cm 71 4.1.3.2 Impeller depth at 16.5 cm and 21.5 cm 72 4.2 Discussion 81 4.2.1 Effect of Impeller Speed 81 4.2.2 Effect of Impeller Depth 82 4.2.2.1 Critical Tip Speed 84 vi 4.2.3 Effect of Impeller Type 87 4.2.4 Effect of Diameter 88 4.2.5 Effect of Baffles 89 CHAPTER 5 SUMMARY, CONCLUSIONS AND RECOMMENDATIONS 91 5.1 Surrimary and Conclusions 91 5.2 Recommendations for future work 96 REFERENCES 97 APPENDIX A 102 APPENDIX B 103 APPENDED C 105 APPENDIX D 108 List of Figures Figure 1 Schematic representation of a horizontal autoclave 2 Figure 2 Models for oxygen absorption during oxidative leaching 1 Figure 3 Mechanisms for ammonia leaching of pentlandite-nickel concentrate 1 Figure 4 Liquid-side mass transfer models 1 Figure 5 Liquid-phase concentration profiles for mass transfer with chemical reaction (Film theory) 1 Figure 6 Schematic diagram for concentration gradient in liquid film for gas absorption with moderately fast simultaneous chemical reaction 1 Figure 7 Mixing impeller types 2 Figure 8 Formation of vortex by impeller agitation 2 Figure 9 Nomenclature used to describe the mixing system 2 Figure 10 The standard tank configuration 3 Figure 11 Power curves for 6-blade flat blade turbine systems with various baffle widths 3 Figure 12 A sectional view of the mixing model 4 Figure 13 Impeller types and dimensions used 4 Figure 14 A detailed diagram of the experimental set-up 4 Figure 15 A typical rate curve for the oxidation of sodium sulphite 4 Figure 16 Plot showing the reproducibility of experimental results 5 Figure 17 Plot showing the reproducibility of experimental results f Figure 18 Effect of impeller tip speed on the rate of oxygen mass transfer f Figure 19 Effect of impeller tip speed on the overall mass transfer parameter ... 53 Figure 20 A plot showing the relationship between power consumption and impeller tip speed 54 Figure 21 Impeller positioning in mixing model 55 Figure 22 Effect of impeller depth on the overall mass transfer parameter at constant tip speeds 56 Figure 23 Effect of tip speed on the overall mass transfer parameter at constant depths 57 Figure 24 Effect of impeller depth on power consumption at constant speeds ... 59 Figure 25 Effect of impeller depth on the mass energy ratio at constant speeds 60 Figure 26 Effect of depth of impeller immersion on the overall mass transfer parameter at constant impeller speeds using an axial pitched-up impeller 61 Figure 27 Effect of impeller tip speed on the overall mass transfer parameter at various impeller depths using an axial pitched-up impeller 61 Figure 28 Effect of impeller depth on the power consumption at various tip speeds using an axial pitched-up impeller 63 Figure 29 Effect of impeller depth on the mass energy ratio at various tip speeds using an axial pitched-up impeller 63 Figure 30 Effect of impeller type on the overall mass transfer parameter 65 Figure 31 Effect of impeller depth on the overall mass transfer parameter for radial 18-cm impeller 66 ix Figure 32 Effect of impeller depth on the overall mass transfer parameter for radial 23-cm impeller 67 Figure 33 Effect of impeller depth on the overall mass transfer parameter for radial 28-cm impeller 67 Figure 34 Effect of radial disc impeller diameter on the overall mass transfer parameter 70 Figure 35 Effect of baffles using a 4-bladed 23-cm pitched-up axial impeller at 11.5 cm depth 73 Figure 36 Effect of baffles using a 6-bladed radial 18-cm disc impeller at 11.5 cm depth 74 Figure 37 Effect of baffles using a 6-bladed radial 23-cm disc impeller at 11.5 cm depth 75 Figure 38 Effect of baffles using a 6-bladed radial 28-cm disc impeller at 11.5 cm depth 76 Figure 39 Effect of baffles using a 6-bladed radial 23-cm disc impeller at 16.5 cm depth 77 Figure 40 Effect of baffles using a 6-bladed radial 23-cm disc impeller at 21.5 cm depth 78 Figure 41 Effect of baffles using a 6-bladed radial 28-cm disc impeller at 21.5 cm depth 79 X List of Tables Table 4.1 Error bar estimates 51 Table 4.2 Comparison of theoretical critical tip speed with experimental estimates for the 6-bladed radial disc impeller (unbaffled case) 58 Table 4.3 Comparison of theoretical and experimental critical tip speeds for a pitched-up axial impeller (unbaffled case) 62 Table 4.4 Effect of impeller type on the impeller power consumption 65 Table 4.5 Effect of impeller depth on the impeller power consumption 68 Table 4.6 Effect of radial disc impeller diameter on the impeller power consumption 70 Table 4.7 Comparison of the theoretical and experimental critical tip speeds for three different radial disc impellers in baffled and unbaffled tanks 80 Table I Mass transfer parameter values 97 xi List of Symbols Agn Gas-Liquid interfacial area (m-1) C* Solubility of component/ at the gas-liquid interface (molelm*) Cf Average steady state concentration of component (molelm2) i (bulk) CNO^O3 Concentration of Na2S03 (mole I m3) Ccosot Concentration of CoSOA (mole/m3) DA Diffusivity of dissolved gas A in the liquid m2/s Da Impeller diameter (m) d lever arm length (m) —— Rate of sulphite depletion (molelm - min) 6/ Stagnant film thickness (mm) ZQ Fractional gas hold-up F Force (N) g Gravitational constant (m/s2) Ha Hatta number ^-^k^C^CS Impeller depth below static liquid surface (m) Impeller velocity head (m) Liquid phase mass transfer coefficient for (m/s) component i Gas phase mass transfer coefficient (mis) Rate constant Mass transfer parameter (min"1) Kinetic constant for hypothetical sulphite (no impurities) Mass difference of liquid displaced by gas bubbles (kg) Impeller speed ( rev I min) Power number Reynolds number Froude number Weber number ptf30o5 PND] pN2Dl Impeller pumping number Q NDl xiii 0 Exposure time of an element to the gas-liquid (sec) interface P\ Partial pressure of soluble gas in the bulk gas (atm) P* Partial pressure of soluble gas at the interface (atm) P Power required by the agitator (Nm/s, watts) Q Impeller pumping rate (m3ls) Ri Mass transfer rate for component i (mole I m2 - min) S Surface renewal frequency (sec-1) T Vessel diameter (m) LI Viscosity (kglm-s) v Tip speed (mis) v* Critical tip speed (mis) VG Superficial gas velocity of the sparged gas (mis) V.P. Volumetric power (wattslm2) co Rate of angular displacement (radlsec) p Liquid density kg/m2 a Surface tension N/m xiv Acknowledgements I would like to express my thanks to my supervisor, Dr. Ernest Peters for his thorough supervision, support and patience that I enjoyed during the course of this research. Also, I wish to extend my sincere appreciation to the technical staff in the department for making their expertise available to me. I owe a debt of gratitude to my fellow graduate students for their numerous constructive criticisms and intelligent comments that helped enrich the study. Special thanks go to NSERC and Cominco Ltd. for their financial support throughout the entire period of this research. Without their support this work would not have been possible. Finally, to my mother and wife goes my deep appreciation for serving as sources of inspiration in my academic endeavors. 1 CHAPTER 1 INTRODUCTION 1.1 Oxygen Pressure Leaching Technology For the past forty years much effort has been directed towards the development of pressure leaching processes, beginning with a theoretical possibility and culminating in technically and economically proven process technologies. Concern about the impact of technological development on the environment has been responsible for a continued interest in metal sulphide hydrometallurgy. This interest is also a result of the prospect that pressure hydrometallurgy can compete directly with roast-leach/roast-smelt processes for recovery of metals from sulphide ores and concentrates, because pressure leaching processes avoid sulphur dioxide emissions and/or the sulphuric acid marketing problems associated with roasting and sulphide smelting operations. Oxidative pressure leaching technologies are directed towards the use of compressed air or oxygen as oxidant, at elevated temperatures, for the leaching of complex sulphides of such metals as nickel, cobalt, copper, zinc, uranium and gold from their ores or concentrates into aqueous solutions. Many oxidants such as ferric iron (Fe3*), nitric acid, peroxide, chlorates, etc, can be used in metal sulphide leaching solutions, but the most available and low cost oxidant often used is air or gaseous oxygen. The use of oxygen provides a much easier way of utilizing the exothermic reaction heat to maintain leaching temperature. It does not contaminate leach solutions in the presence of a variety of anions, and it reacts with the sulphides of many metals to produce sulphates or elemental sulphur. 2 The applications of higher reaction temperatures and pressures have been established to accelerate most oxidative pressure leaching reactions. One notable achievement under these conditions in commercial application is the recently implemented oxygen-sulphuric acid leaching process of Zn concentrates at Cominco, Trail, B.C. and at Kidd Creek mines in Ontario. Figure 1 shows a typical four-compartment autoclave designed for continuous leaching operations used in both the above applications. Similar units are used in all Sherritt's pressure hydrometallurgical processes, although they vary in the number of compartments. Figure 1 Schematic representation of a horizontal autoclave The dissolution of metal sulphides in oxidative pressure leaching is usually modelled as an anodic process [ 1]. When a metal sulphide is placed in contact with a solution containing an oxidant (eg. Fe3* in acid solution or Cu (NH3)2+in alkaline solution) having a more positive equilibrium potential, a corrosion cell can result in the anodic oxidation of metal sulphide (MS) and a cathodic reduction of the oxidant (7V+) according to the equations: 3 MS -^Mn+ + S°+me~ (1.1) Nn+ + e~ ->N(n~x)+ (1.2) Oxidative pressure leaching of metal sulphides results in the formation of metal ions in the aqueous phase and the liberation of elemental sulphur according to the reaction: MS + 2H++l/202-*M2+ + S°+H20 (1.3) Elemental sulphur so produced may be further oxidized to form sulphate by oxygen or other oxidants present in the leach solution. 25° + 302+2H20 -> 4H+ + 2S02~ (1.4) S° + 6Fe3+ + 4H20 6F<?2+ + 8/7+ + S<942~ (1.5) Therefore, the oxidative pressure leaching of sulphides has been proposed as an alternative to the conventional roast-leach operations. 1.2 Concept of Oxygen Utilization in Oxidative Pressure Leaching Processes In oxidative pressure leaching, a high oxygen absorption rate is an important requirement in most metal dissolution processes. To achieve high rates, the pressure leaching reactors (autoclaves) have been designed with very high sparging and agitation rates and also with a capability of handling high temperatures and pressures. Spargers are primarily used to introduce oxygen bubbles into the autoclave, but because these bubbles are "one pass bubbles", not all the oxygen is absorbed before the bubble breaks the surface of the slurry. The remaining oxygen that enters the plenum space above the slurry must be 4 discarded, or recycled to the leach solution by gas pumping agitation. Such gas pumping agitation creates bubbles of gas that are drawn from the vortex (created by the agitator motion) down into the impeller zone, and then dispersed in the pulp. For oxygen to be consumed, it must dissolve, or alternately, form a surrogate oxidant with a reducing agent at the gas-liquid interface, after which mass transfer of the dissolved oxygen (or its surrogate) to the suspended mineral particle surface takes place. Recent developments have indicated high oxygen consumption rates of about 35 g-mole/m3-min during oxidative pressure leaching. In the case of zinc concentrates, the process is not commercially viable if the oxygen consumption rate is much lower than 7.5 g-mole/m3-min [2]. At such high oxygen consumption rates, the mass transfer of dissolved oxygen at the gas-liquid interface may become rate-limiting. Therefore, it is desirable to have a better understanding of the gas-liquid mass transfer process that occurs in oxygen pressure leaching. Peters [2,3] has offered various models for the absorption of oxygen during oxidative leaching. These models fall into 4 distinguishable mechanisms: 1. Oxygen dissolves, then is transported as a solute through the solution to the particle surface where it is consumed at the solid-liquid interface. 2. Homogeneous reactions transform dissolved oxygen into a surrogate oxidant whose concentration builds up and this oxidant is then transferred (more rapidly than oxygen) to the mineral particle surface. 3. Oxygen may react at the gas-liquid interface with a reducing agent whose product is a surrogate oxidant that reacts at the mineral surface. 4. Oxygen may react in the gas phase to generate a much more soluble gaseous surrogate oxidant, which dissolves much faster than oxygen, and is transferred as a solute to the mineral surface. 5 These 4 models are shown ^grammatically in Figure 2. In the first model, Figure 2(a), oxygen will dissolve when there is no aqueous reductant at the bubble surface capable of having an instantaneous reaction with oxygen. The dissolution rate is given by the equation: Agn = gas-liquid interfacial area The solubility of oxygen in water ranges from 0.8 to 1 g-mole/m3.atm. Due to its poor solubility in aqueous solutions, oxygen dissolution is a fairly slow process. Studies [4] done on the cathodic reduction of oxygen on minerals at both room temperature and under autoclave conditions have proven that the electrochemical reduction of oxygen at mineral surfaces is too polarized to take place at useful rates, even at elevated oxygen pressures where dissolved oxygen is present at appreciable levels. However, in the presence of bacteria such as thiobacillis thio-oxidans, the oxidation of sulphide minerals by dissolved oxygen can be catalysed to useful rates. Dissolved oxygen may also react homogeneously with reducing agents such as Fe 2 + present in solution, and create a secondary oxidant (surrogate oxidant) at the mineral surface as described in the second model. The oxygen mass transfer rate in this model is also given by equation (1.6). However, oxygen transfer to the mineral surface is replaced by transfer (1.6) k02 = liquid side mass transfer coefficient for oxygen C*0 = solubility of oxygen at gas-liquid interface CQ2 = average steady-state oxygen concentration 1 the gas side mass transfer resistance is so small it can be neglected. 6 of the surrogate oxidant which appears at much higher concentrations. A typical example is zinc pressure leaching, where the dissolved oxygen is known to react with Fe 2 + ions according to the equation: 4Fe2+ + 4H+ + 02^>4Fe3+ + 2H20 (1.7) The surrogate oxidant, Fe3+ ions, can then be transported to the mineral surface (ZnS) at the rate proportional to its concentration. Figure 2(b) shows a generalized case where R represents the dissolved reducing agents and R+ the surrogate oxidant. At the mineral surface, the oxidant (R+) is available at a much higher concentration than dissolved oxygen, and because of this a faster reaction rate is observed in this model than the first. It is also possible to have a catalysed reaction between Fe 2 + ions and dissolved oxygen under bacterial leaching conditions. The third model, Figure 2(c), replaces the processes at the gas-liquid interface. Oxygen may be rapidly consumed at the gas-liquid interface if a sufficiently reactive reducing agent (R) generated by the mineral decomposition reaction is presented to the oxygen bubble. A typical example involves the ammoniacal systems where cuprous ammine (Cu(NH3)*) is known to oxidize extremely rapidly, even at room temperature [5]. This Cu (NH3)2 reductant might be far more reactive to oxygen than Fe 2 + ions. Due to its rapid oxidation at the gas-liquid interface, oxygen dissolution is overtaken by the rate of mass transfer of Cu(NH3)^ to the bubble surface, and so dissolved oxygen is not available for further reaction. The oxidation product, cupric ammine Cu(NH3)2+ then acts as a surrogate oxidant at the mineral surface. If the diffusion of Cu(NH3)2 to the oxygen bubble surface is to be the rate-determining step, the mass transfer equation becomes: / ? 2 = Mw , ( c f -c ; )=VCf (1.8) 7 Agll = the gas liquid interfacial area C\ = concentration of Cu(NH3)2 in bulk solution C* = Cu(NH3)2 concentration at the interface (= 0) kt = liquid side mass transfer coefficient of CuiNH-^ The following equations illustrate the oxidation at the bubble surface, and reduction at the mineral particle surface: at the bubble surface 4Cu(NH3)+2 + 02 + 4NHi+(n - l2)NH3-^4Cu(NH3ftt+ + 2H20 (1.9) at the mineral surface 3Cu(NH3fn+ + CuFeS2 -> 4Cu(NH3)+2+Fe2++2S° + (3n - S)NH2 (1.10) Also, Cu (NH2)l+ is a surrogate oxidant for the homogeneous oxidation of Fe 2 + released from the mineral decomposition and for unoxidized sulphur species formed by the non-oxidative dissolution of sulphur in ammoniacal solutions. About 80% of the oxidant formed is consumed through homogeneous reactions and not more than 20% is reduced at the mineral interface by reactions such as equation (1.10). In the Anaconda-Arbiter process, Cu(NH3)2n+ is the surrogate oxidant at the mineral surface, and dissolved oxygen is completely absent under normal conditions. This process obtains perhaps the most rapid oxygen absorption rates due to the significant concentrations of Cu(NH3)l in the leach liquor. An oxygen consumption equivalent to 120 kg/m3 has been observed based on a 5-hour residence time. At this rate almost all the sulphur in the copper concentrates may be oxidized to sulphate with a system pressure of only_35^ atm [6]. 8 Forward and Mackiw [7] earlier proposed a model (Figure 3(a)) for the ammonia leaching of nickel based on the leaching of pentlandite by dissolved oxygen diffusion, through an iron oxide layer, as the rate-controlling step. This model requires the transport of dissolved oxygen through the porous hydrated ferric oxide layer to reach the mineral and oxidize the surface. However, from the above discussions, oxygen dissolution is found to be relatively slow, and so the reduction on these mineral surfaces is too slow to support practical mineral decomposition rates, or to compete with Cu(NH3)2n+ if these are present. The leaching mechanism of pentlandite-nickel concentrate can be covered by Peters' third model, because copper is always present in nickel concentrates. Therefore, the generation of Cw(M/3)2 is quite possible during ammonia leaching of pentlandite-containing nickel concentrates. Since Cu(NH3)* is known to react very rapidly with oxygen, the rate-determining step will probably be the diffusion of the Cu(NH2)* species to the oxygen bubble surface, and Cu (iV//3)2+will be the surrogate oxidant, both to homogeneous reactions and for oxidizing the mineral surface. This mechanism is represented diagrammatically in Figure 3(b). The fourth model shown in Figure 2(d) describes the generation of a soluble surrogate oxidant in the gas phase identified as Q0 2 , which leads to a more rapid oxygen mass transfer process if the solubility of Q0 2 is higher than that of 0 2 (see equation (1.6)). This model forms the basis for the Arseno, Nitrox, and REDOX processes for gold ores [8]. N0 2 is the gaseous surrogate, and this converts to NO + (a protonated form of HNOz) in solution. HN0 2 is used as a very active oxidant for this process and is useful for processes that require rapid sulphur oxidation2. 2 Note that HN03 is several orders of magnitude less reactive than HN02 [8] 9 In the first three models, the value of the gas-liquid interfacial area (A^ = m2/m3 or m"1), which is always proportional to the oxygen mass transfer rate, is maximized by sparging and gas pumping agitation3. In view of this, an appropriate agitator design is important in the oxygen pressure leaching process, where gas-liquid mass transfer is rate-Umiting. The aim of this investigation was to evaluate the effects of the various process variables that enhance the rate of oxygen mass transfer across the gas-liquid interface. As previously discussed, the value of the gas-liquid interfacial area Ag/t is always proportional to the oxygen mass transfer rate. This in turn is maximized by sparging and gas pumping agitation and because of this, emphasis has been placed on the creation of gas-liquid interfacial area in mechanically agitated vessels by only gas pumping agitation. It was therefore important to consider the following process variables: 1. To examine the influence of impeller speed on the oxygen mass transfer rates. 2. To evaluate the impeller depth for effective oxygen gas dispersion. 3. To determine the most efficient impeller type and size for gas dispersion necessary to produce many small gas bubbles capable of increasing the interfacial area . 4. To assess the role of baffles in the enhancement of gas-liquid mass transfer rates per volumetric power. Power consumption, which is an important factor for evaluating the process viability in terms of energy efficiency, was considered. The mechanism by which gas dispersion takes place may differ from that of fluid mixing, hence, the conditions that optimize gas dispersion in gas-liquid systems may be different from fluid mixing. Therefore, it is necessary to establish a clear distinction between these two phenomena. The usefulness of 3 However, it may be that surfactants that increase the value of are not productive because they may lower the value of k0i at the same time [9,10] 10 dimensionless correlations for scaling-up a gas-liquid mass transfer systems was also important in the study. Since over 75% of the leaching reaction in the oxygen pressure leaching process typically takes place in the first compartment, aphysical model representing the first stage of the industrial autoclave was employed in this study. The ultimate goal of this work was to establish a theoretical basis for predicting the mass transfer parameter, Kg, because it is needed in the modelling of hydrometallurgical systems that involve gas absorption. 11 Dissolved Metal Figure 2 Peters' models for oxygen absorption during oxidative leaching [2] 12 Gas phase Fe O xH O 2 3 2 Model (a): Forward & Mackiw Gas phase o 2 Model (b): Peters, E. Figure 3 Diagrams showing two distinct mechanisms for ammonia leaching of nickel (penUandite concentrates) 13 CHAPTER 2 LITERATURE REVIEW 2.1 Mass Transfer in Gas-Liquid Systems 2.1.1 Physical absorption Three different models [11], shown in Figure 4, have been used to describe gas absorption (mass transfer) from bubbles where the different expressions for kh the physical liquid-side mass transfer coefficient, apply in the absence of chemical reactions. The film and the surface-renewal models fall under physical absorption where dissolved gas molecules cannot be divided into reacted and unreacted categories (gas dissolves in liquid without reacting). The transport of the solute gas relies on the concept of additivity of a gas-phase resistance and a liquid-phase resistance, assuming a negligible interfacial resistance. The absorption rate may be given by: R = kgAgll(P>-P*) = ktAg/l(C*A - CAo) (2.1) where kg is "true" gas side mass transfer coefficient, kt is the liquid-side mass transfer coefficient, Ag/, is the interfacial area between gas and liquid per unit volume of solution; P\ and P\ are the respective partial pressures of soluble gas in the bulk gas and at the interface, CA is the solubility of gas at the given partial pressure in the gas bubble and CAo is the steady state concentration of dissolved gas in solution (when the concentration of dissolved gas and liquid are statistically constant when averaged over time in a specified 14 region). It has been established that the mass transfer resistance in the gas phase for bubbles passing through liquids may be ignored compared with the much higher resistance offered by the liquid phase [12]. In the film model a stagnant film of thickness 8, is assumed at the liquid surface next to the gas, while the liquid bulk concentration is kept constant by turbulent agitation [11]. This model predicts that kt is proportional to DA, the diffusivity of the dissolved gas in the DA liquid where kt = The surface renewal models assume the periodic replacement of elements of liquid at the interface by liquid from the interior, of mean bulk composition. Such a phenomenon is achieved by turbulent circulation of the liquid. The original model proposed by Higbie [11] assumes that every element has an equal length of time 8 to be exposed to the gas before being replaced by liquid of the bulk composition. Therefore, the elements absorb equal amount of gas per unit area where kt = ^ {^J- Danckwerts' model [11,13] disagrees with Higbie's uniform time model especially in industrial gas-liquid contactors. He claims that the probability of an element being replaced by fresh eddies at the interface is independent of the length of time for which it has to be exposed, where kt is given by kt = (DASf. The hydrodynamic properties of the gas-liquid system depend on the geometry of the vessel, physical properties, and liquid agitation. These properties are accounted for by film thicknes s 8, in the film theory, 0 in Higbie's model and S, the surface renewal frequency in the Danckwerts' model. The models of Higbie and Danckwerts make a better prediction for kt than the film model since experimental observations on kt are found to vary as DA. However, these models can be used interchangeably to suit several purposes. Computations relating to the film models are easier to deal with than the other two models. 15 Gas Liquid film film i Film model Higbie model Danckwerts model in the in the liquid in the liquid liquid Figure 4 Liquid-side mass transfer models 2.1.2 Mass transfer with chemical reaction The film theory of mass transfer can be used to describe gas absorption with simultaneous chemical reaction. Let a gaseous compound A transfer into a solution where it reacts with a non-volatile solute B according to: A ( g ) + zB —> products (2.2) Several assumptions are made in the film theory: plane interfacial area, steady state conditions, film of thickness, 8, constant throughout the vessel and convection neglected within the film. A dimensionless parameter called the Hatta number (Ha) has been developed as a measure of the contribution of the chemical reaction in the transfer of A. Also, it provides 16 an indication whether a large specific interfacial area A n or a large hold-up is required for a particular reaction. For a chemical reaction of order m with the rate constant k^, the rate of chemical reaction is k^C^C^, and the Hatta number is given by: k~i y (m + 1) (2.3) where CA, CB are the concentration of A andB respectively. Assuming a first order reaction with respect to species A, the film theory [11,14] leads to the following transfer rates: RA=-\IPA = -k,A dx Ha g"th(Ha) : = 0 c:- ch(Ha) (2.4) (2.5) in which the Hatta number is given by Ha=^^k~p^B (2.6) When Ha is small (<0.02), no reaction occurs in the film. Mass transfer is used to keep the bulk concentration of component A, CAo, close to the saturation CA Figure 5(a). ^ = M , / / C ; - Q 0 ) (2.7) In a slow reaction (0.02 < Ha < 0.3) process, a physical absorption is followed by reaction in the bulk liquid as shown in Figure 5(b). This type of reaction is too slow to affect the rate of absorption directly but not too slow to keep the bulk concentration of the dissolved gas CAo close to zero. *A~M, /A* (2.8) 17 ( a ) i n t e r f a c e B u l k L i q u i d Liquid film j I n t e r f a c e Liquid filn (b) B u l k L i q u i d H a < 0 . 0 2 H a < 0 . 3 Figure 5 Liquid-phase concentration profiles for mass transfer with chemical reaction: Film theory Both interfacial area and liquid hold-up should be high for this slow reaction situation, so the use of a mechanically agitated tank would be suitable. Equation (2.8) means that the rate of transport process is completely determined by the mass transport across the liquid film. The mass flux through the interface is proportional to ktAgn. This result is the basis for using a chemical reaction to measure ktAgH directly from the rate of absorption when C*A is known. In a moderately fast reaction (0.3 < Ha < 3.0), Figure 6, a substantial amount of component A reacts in the film instead of being transferred unreacted to the bulk liquid. The concentration CAo approximates zero due to fast reaction in the film. RA * kA^HaC: = AtllcUKJ>ACHB (2.9) It can be seen from equation (2.9) that the absorption rate of A is independent of the mass transfer coefficient kh and only depends on a chemical factor, k^, and a physical property of the system, DA. Both properties are independent of the hydrodynamic conditions 18 or degree of agitation and therefore, measurements of chemical absorption rates under conditions of known CB, andDA can be used for a direct determination of the interfacial area Ag/l. In this model for example, oxygen entering the liquid phase reacts completely within the film at the interface. In other words, the hydrodynamic conditions (which depend on impeller speed) prevailing in the liquid phase have no influence on the absorption rate. Therefore, this model calls for a constant absorption rate with impeller speed. However, the absorption rate varies directly with Ag/l. interface ^Liquid film Bulk Liquid CBO Bulk Gas * CAO=0 0.3<Ha<3.0 Figure 6 Schematic diagram for concentration gradient in liquid film for gas absorption with a moderately fast simultaneous chemical reaction. 2.1.3 Gas-liquid interfacial area When a gas forms a dispersion in a liquid, knowledge of interfacial area is frequently important in determining the corresponding mass transfer coefficient. For an ideal dispersion consisting of equal spherical bubbles of size DBm, the interfacial area, Ag/l, per unit volume of dispersion [15] is given by: 19 \n = t>-y- (2.10) where e<; = gas hold up or volume fraction of gas in the dispersion. An increase in the interfacial area is mainly the result of an increase in the fractional gas hold up (0.4 typical upper limit) when the average bubble size is essentially constant over a range of agitation rates. The size of gas bubbles produced in a gas-liquid dispersion is determined by the hydrodynamic conditions, when a balance is reached between surface tension forces and those due to turbulent fluctuations. The gas hold-up, interfacial area and the mass transfer coefficient are considered the main variables that determine the mass transfer rates in gas-liquid systems. Two methods are used to measure these parameters: Local measurements with physical techniques such as light scattering or reflection, photography, or electric conductivity and global measurements with chemical techniques. The light transmission and chemical methods are the most widely used. The literature [11,15,16,17,18] has clearly established the descriptions and systems used for such measurements. Calderbank [15] determined local values of the gas hold up and of the interfacial area and found that both were strongly dependent on the position in the vessel. Westerterp et al [19] also observed that very near to the impeller many very small bubbles and thus high interfacial area are created. However, when the dispersion is pumped away from the direct neighbourhood of the agitator, the growth of the gas bubbles (due to coalescence) diminishes the local specific interfacial area. The coalescence rate increases as the gas bubbles are withdrawn from the action of the impeller and get farther away from the impeller. Preen's [20] work concluded that practically all disintegration takes place in the neighbourhood of the impeller and that coalescence occurs further away in the vessel from the point of agitation, especially between bubbles with a small diameter (<0.5mm) and large diameter (>3mm). i 20 Also the final value of AgU is determined by coalescence and not by disintegration. The presence of small quantities (about 0.05%) of hydrophilic solutes in an aerated mixer have been found to increase the interfacial area by a large factor and does exert a profound effect on the ease with which gas bubbles coalesce [9,10,15]. With water containing a small amount of say, alcohol, no coalescence was ever observed, but with water containing no solute, the bubbles coalesced immediately on contact to form large bubbles which eventually burst. It was found that small bubbles give much smaller values of kt than larger bubbles. Observations made by Mehta et al. [10] have established that an increase in the ionic strength and the viscosity or a decrease in surface tension of the medium increases the effective interfacial area. Also, the presence of an immiscible phase increases the effective interfacial area marginally. 2.2 Liquid Mixing and Agitation Fluid mixing is at the heart of most hydrometallurgical leaching operations and is defined as the random intermingling of two or more phases, resulting in the attainment of a desired level of uniformity, either physical or chemical in the final product. Agitation on the other hand involves the creation of a state of activity such as flow or turbulence, apart from any mixing accomplished [21]. Mechanical agitation is often used to keep the particles in suspension, thereby exposing all of the available surfaces to lixiviant. It also serves to increase mass transfer by increasing the transport of reactants and products to and from reaction sites. The associated shear action tends to decrease liquid film mass transfer boundary layers. The agitator tip speed (v) is commonly used as a measure of the degree of agitation in a liquid mixing system. This is given by, v = —— x rpm ms (2.11) 21 where Da is the diameter of the agitator in meters and rpm is the rotational speed of the agitator in revolutions per minute. A study of the mixing process includes several basic considerations, such as the effect of the vessel on the mixing process, the type of mixing impeller, or impellers to be used for a given process and the effect of baffles in mixing vessels. Vessel geometry, dimensions and structure may dictate mixer selection and mixing performance. In leaching, much attention is focused on the rate of attainment of specified quality of end product from a given amount of feed material, and as such a satisfactory reactor design is necessary for the mixing process. There are basically three ideal reactor types; the batch, the backmixed and the plug flow reactors. 2.2.1 Basic reactors In a batch reactor, reactants are brought together, mixed and allowed to react over a period of time. The mixture is then discharged and a new batch brought in. At steady state condition the composition is constant throughout the reactor. The composition in the reactor changes with time during unsteady state processes. The backmixed reactor is also known as the constant flow stirred tank reactor (CFSTR). Material in this reactor is well stirred and therefore of uniform composition. The fluid leaving the reactor and the fluid inside the reactor have the same composition. In a plug flow reactor all elements of fluid entering the reactor have the same residence time with that inside the reactor. The fluid composition changes with distance along the reactor. The performance of these reactors can be predicted by accounting for the following two sets of constraits: i. Rate constraints; mass transfer, heat transfer and reaction kinetics. ii. Reactor-imposed constraints, e.g., reactor type, geometry, etc., and incorporating them into a design equation by means of material and heat balances [22]. 22 2.2.2 Impeller types There is an infinite choice of impellers for any mixing operation. Considering them as either radial or axial flow impellers (up or down), however, enables certain unifying features of each to be selected. Two of the most commonly applied axial-flow impellers are the marine propeller and the axial flow turbine (also called the pitch blade turbine) shown in Figure 7(a&b). They generate their maximum flow parallel to the impeller shaft, along the impeller axis. Radial-flow impellers such as turbine impellers as shown in Figure 7(c), act by centrifugal action and direct fluid away from the shaft. The choice of impeller type depends on the desired process result, e.g., (i) gas dispersion (ii) reactions in solution (iii) dissolution (iv) solids suspension. The turbine type impellers which may be either open or center-disk are the most versatile choice for most hydrometallurgical mixing needs. For gas-liquid applications, it is necessary that gas bubbles are kept in the liquid as long as needed. Thus, propellers are generally unsuitable because of their axial flow characteristics. Turbine impellers are most effective because of their ability to provide radial flow circulation. Since the lowest fluid velocity is immediately below the center of the shaft when gas is introduced below the impeller, a sufficient distance must be provided below the shaft if gas is not to escape from the circulation pattern. The centered disk turbine is particularly useful for gassed systems, because the disk prevents the premature escape of gas. The main disadvantage of the center-disk turbine is that it is limited to viscosities < 20,000 cp. due to the tendency to produce stratification rather than mixing [22,23]. 24 2.2.3 Tank baffles Axial-flow or radial-flow impellers in unbaffled tanks containing low viscosity fluids tend to swirl and produce vortices in the direction of the agitator motion, causing a drop in liquid level around the agitator shaft. These vortices shown in Figure 8, keep on increasing with impeller speed until they pass through the agitator. Agitators in this condition are poor mixers, but good gas dispersers. Installing baffles destroy the vortices and promote a flow pattern conducive to good mixing. Adequate baffling assures good mixing by providing a flow pattern that is carried throughout the entire batch. Excessive baffling (or over baffling) will reduce the mass flow and will localize the mixing and may result in poor process performance. With viscous liquids, baffles are most effective when positioned away from the tank wall or at an angle to the axis of symmetry of the vessel. o o Figure 8 Formation of vortex by impeller agitation. 25' 2.2.4 Impeller location and proximity The Figure 9 illustrates the nomenclature used to describe the mixing system: 1. Impeller off bottom distance C is measured from the lower impeller's horizontal center line to the lowest point on the tank bottom. Flat bottoms, shallow cones, hemispherical bottoms etc., are treated in the same manner. 2. Impeller depth CV is measured from the static liquid surface to the horizontal center line of the upper or lower (single) impeller. 3. Spacing between impellers S is measured from impeller horizontal centerline to the next. 4. Liquid depth Z is measured from the static liquid surface to the lowest point on the tank bottom. A depth of approximately two impeller diameters has usually been used in most mixing operations. When impeller depth is reduced to one diameter or less, a critical impeller depth may be reached beyond which the flow pattern developed by the impeller may become unstable. This will increase the fluid forces. The most important factor in flow symmetry and its effect on fluid forces is the proximity of the impeller to the boundaries of the system. The dimension that is used in describing proximity is the diameter of the mixing impeller to tank diameter ratio. The boundary has little effect if it is more than two diameters away from the impeller. As the boundary becomes less than one diameter away from the impeller, its influence on the forces becomes significant [23]. 26 Figure 9 Nomenclature used to describe the mixing system 2.3 Gas Pumping and Dispersion by Agitators The work of Westerterp et al. [19] involving sparging to supply a gas flow indicates that the gas hold-up and the specific interfacial area are essentially dependent on the gas flow rates at low impeller speed, while at high impeller speeds they depend upon the impeller speeds. Thus, the agitator is fully effective in dispersing the gas into the liquid only at high speeds of agitation. It has been found that there is a transition region between the two, where both the gas flow rate and the impeller speed are important. Conclusions were drawn to relate critical agitation speed N0D to a point where effective gas dispersion is realized. N0D 27 becomes smaller as the impeller blades approach the baffles and the vessel wall (T/D smaller). It was further explained that, for a minimum agitation rate to occur the impeller tip velocity must exceed the gas rising velocity by a certain number of times (about 30) in order that all big gas bubbles supplied can be broken up into small bubbles. The following equation was proposed by Westerterp et al. [19] and accepted by others [10,24,25] for the prediction of the minimum speed of agitation, beyond which only impeller speed is important "Hi) - M S (2.12) Where T is the vessel diameter, p is the liquid density, a is the surface tension and g is the gravitational constant. A and B are constants and are functions of agitator type. The following has also been proposed by Pandit et al. [26] to predict the critical agitation speed based on the liquid circulation velocities. NM 1 (TV = .865 L\ I . O (2.13) Where T is the vessel diameter in meters, VG the superficial gas velocity of the sparged gas, and EG is the fractional gas hold-up. The above models have been shown to correlate well under the conditions where they were applied. However, their universality is limited due to the fact that an important factor, the effect of impeller depth of immersion was completely neglected in both models. It is quite obvious that the critical speed will differ with impeller position within the vessel. Also, in equation (2.13) it is hard to accept that if no gas is sparged (VG = 0) the critical speed will never be attained. This is contrary to experimental evidence [5]. 28 Peters [27] has postulated a separate approach for a gas pumping agitator taking care of the depth of impeller immersion, to predict the critical agitation speed which is based on a simple energy balance. The assumption made was that, if viscous forces are neglected, the critical agitation rate can be approximated on the basis of momentum transfer only and then the kinetic energy needed to generate a gas bubble at the blade tip of an impeller (immersed at a depth h in the liquid) should be equal to the potential energy a gas bubble possesses when drawn to depth h below the liquid surface. Therefore, the energy balance is given by, 1 2 mgh =-mv (2.14) where m is the mass difference of liquid displaced by the gas bubble, and v is the impeller tip speed. Rewriting equation (2.14) in terms of the critical tip speed, V--SS*£ (2.15) a where a represents the impeller efficiency. For an ideal case a = 1. Since this equation is independent of mass (no density effect), it can be applicable in liquid mercury. DeGraaf [5] reported a good correlation of his results with equation (2.15) and he found that the 6-bladed radial disc turbine agitator was the closest to ideal behaviour (value of a = 0.997). 2.4 Impeller Power Requirement The generation of circulating currents in a liquid requires expenditure of mechanical energy which is a function of impeller speed N, diameter Da, the impeller design itself, and a number of mixing environmental factors including: 1. Physical properties of the liquid medium. 2. Vessel size and geometry or shape. 29 3. Impeller location relative to vessel and fluid boundaries, and relative to other impellers or obstructions in the mixing vessel. 4. The presence or absence of baffles, their design, and location. These are the major variables of practical significance. The relationship of power consumption to the physical variables of a liquid mixing system may be developed in terms of several dimensionless groups [21,23]. For an impeller of diameter Z)fl, rotating at N rev/sec in a fluid of density p and viscosity \i, if the power required by the agitator is P, the foremost dimensionless groups are: PR Power number, NP = — f - r (2.16) n Ar PNDZ Inertial force Reynolds number, NRe = = — (2.17) [i viscous drag force „ , • , N D* Inertial force Froude number, NFr = = — (2.18) g gravitational force For a two liquid phase system where a is the interfacial tension, an additional dimensionless group is used, u . A r pN2Dl Inertial force Weber number, NWe = = — J-— (2.19) a surface tension force It is assumed that dimensions such as the height of the liquid in the tank, the diameter of the tank, the number, size and position of the baffles are all strictly related to the agitator diameter. The general relationship between the power number and the other dimensionless numbers is given for multi-liquid phase systems by, Np = C(NRe)x(NFr)y(NWey (2.20) 30 where C is an overall geometric shape factor and x, y, z are constants. When a single liquid phase is involved, equation (2.20) reduces to Np = C(NRJ(NFrY (2.21) Furthermore, in baffled systems, gravitational effects, represented by NFr become negligible so that Hp=C(NRe)x (2.22) A plot of Np against NRe is termed a power curve. The form of the power curve varies, depending on the geometry of the mixing system. A "standard" tank configuration proposed by Rushton et al. [28,29] to facilitate the design of agitated vessels is shown diagrammatically in Figure 10. The power curve which corresponds to the standard tank geometry is presented in Figure 11. The power dissipated by impellers at various speeds in pure liquids may be derived readily from published Power number/Reynolds number plots. 31 Figure 10 The Standard Tank Configuration. REYNOLDS NUMBER N R e , dimensionless Figure 11 Power curves for 6-blade flat blade turbine systems with various baffle widths. 33 2.4.1 Power correlations An impeller is essentially a pump and has many of the same characteristics of a pump. This can clearly be examined by the following relationships which apply for impellers in turbulent flow (i.e. NRe > 104). Impeller pumping capacity Q=NQND3a (2.23) Power output NnpN3D! P = — - (2.24) 8 Impeller velocity Head p N N2D2 PQ NQg where NQ is flow number, N is impeller speed in rpm, Da is impeller diameter, NP is power number, and g is acceleration due to gravity. Equation (2.24) depicts the high sensitivity of power to impeller diameter and to speed. 2.4.2 Power reductions through gas sparging and entrainment of gas The introduction of gas immediately below the rotating agitator is dispersed throughout the vessel. The gas reduces the density of the agitated mass and hence the power required. In liquid mixing the slurry density can safely be assumed to be nearly constant, which allows the use of dimensionless parameters such as Reynolds number (NRe) and the Power number (Np) to predict the power consumption, degree of agitation etc. However, in gas dispersion which involves gas pumping by the agitator, the slurry density is lowered by dilution with gas bubbles due to entrainment of gas in the liquid. In view of this the slurry density throughout the solution cannot be assumed to be constant. The impeller also pumps gas into the liquid from the gas plenum aside from breaking up the sparger bubbles. 34 Therefore, the use of a Power number for such system will always predict a higher power consumption than that which is actually required. For this reason the optimum conditions for achieving gas dispersion may be different from that for fluid mixing. 2.4.3 Power measurement Measure of power depends on the torque produced by a rotating agitator. Newton's third law, which states that an action is opposed by an equal and opposite reaction, forms the basis for the operation of torque measuring instruments. One of the methods for measuring torque is by mounting an entire drive unit on a thrust bearing above the liquid in a vessel. The rotating agitator imparts a mechanical force which is opposed by the liquid. The liquid in turn produces a torque on the agitator which is transmitted through the drive shaft to the motor. This reactive torque tends to cause the drive unit to rotate on the thrust bearing in the opposite direction to the agitator rotation. This enables the torque to be measured by transmitting the force through a mechanical linkage such as a spring balance, a load cell, etc. An alternative method is by mounting the mixing vessel on a thrust bearing. Here, the torque produced is measured as the reaction of the vessel to the rotating agitator, the liquid acting as a transmitting medium. The power from the measurements described is given by, Power = Torque x Rate of Angular Displacement P = (Fxd)x(o (2.26) where F is force in Newtons (N), d is lever arm length in meters (m), co is the rate of angular displacement in radians/sec and P is the power in N-m/sec (watt). Since 2K radians is equivalent to one revolution, then 35 (H = 2KN %rpm 30 ( rad^ ^ sec j (2.27) Power, P=(Fx d)^^-(watts) (2.28) 2.5 Overview of Past Work on Oxygen Mass Transfer 2.5.1 Sodium sulphite oxidation The absorption of oxygen by sodium sulphite solutions in the presence of Co 2 + or Cu 2 + ions as catalyst has been used by a number of investigators [32-46] to study the characteristics of mass transfer with simultaneous chemical reaction. Despite the extensive literature on the reaction of oxygen with aqueous sulphite under various conditions of practical interest, clear and accurate kinetic data are lacking. Moreover, numerous studies cast doubt on the suitability of sulphite oxidation to the aforesaid use. Nevertheless, some attractive advantages of the aqueous sulphite (its economy for large scale equipment, lack of toxicity, etc.) have encouraged efforts towards developing a reliable method for mass transfer determination based on this system [34]. The most significant feature of the oxygen-sulphite reaction is its marked sensitivity to catalysts such as, Co 2 +, Cu 2 + , Fe2 +, Mn 2 + , etc.. There is, however, confusion over the "true" reaction mechanism, the nature of the rate controlling process and consequently over the interpretation of the reaction rate results. Opinions differ as to whether the mass transfer coefficient is or is not affected (increased) by the accompanying chemical reaction. Even though a number of models exist that describe the mass transfer between gas and turbulent liquid in simultaneous reactions, they fail to attain a solution to this problem because the application of these models requires a 36 quantitative expression for the reaction rate. Also, there are large discrepancies for closely similar experimental conditions, on the orders of reaction with respect to the reacting species and different conditions under which the reaction order in oxygen is subject to change. To the present day, the kinetics of oxygen-sulphite reaction are still insufficiently understood [35,36,37,38]. The catalyzed oxidation of sulphite to sulphate is not the simple, one step oxidation shown in the stoichiometric equation, SO]'+\°2-+ S0T (2-29) On the contrary, it is known to be a chain reaction of unusual length. A free radical mechanism was proposed by Backstrom [38] and later used by several investigators [33,39,40] to explain the SO2' oxidation in aqueous solutions using Cw 2 + or Co2* catalyst. His scheme includes the metal complex ions [M] as the initiator. initiation, S<93 +[M] -> ,SO;+[Mc] (2.30) propagation, .S03 + Oz -> .SOs (2.31) .so;+sol' -> so2~+.so; (2.32) followed by, S02s' + SOl' -> 2S02'. (2.33) Termination, .SO; + .SO; -> 2S02~+02 (2.34) where [Af] is C o 3 + or Cu2+ and [Mc], is Co2+ or Cu+. Reinders [41] also assumed a free radical chain mechanism for reaction with cobaltous ion catalyst as: 37 Co2+ + SOl~, \ Complex (2.35) k_xfast Complex+ 02 -> S02s~ + Co2+ (2.36) S<92~+S02- ->>2S<92_ (2.37) The formation of a cobalt complex in solutions of sodium sulphite has been shown from ultra-violet spectra [41,42]. Dewaal et al. [43,44] measured the absorption rate for pure oxygen at atmospheric pressure, based on the simple reaction in equation (2.29), where the rate expression is given by, R02 = kmnCoCsa^O^CoSO^ (2.38) where R0i is the reaction rate, km is the rate constant, C0i, CNa^o3 and CCoSOi are the concentrations of 02, Na2S03 and CoS04. The constants, m, n, q are the respective reaction orders. The following are the experimental conditions employed. 3xlQT2mole/m3<CCo2+<0.1mole/m\ 15<T<33°C, 7.5<pH<8.5, CNa2so3 + CNa^0, = 0AKmolelm\ 0.2 < P0i < 0.8 - Xatm, 0.4 < CNaSOj < 0.8M It was reported that, the reaction rate was zero order in sulphite (n=0), first order in cobalt (<7=1) and increased considerably with increased pH and temperature. At lower sulphite concentration (<0.4 M) the reaction rate was found to depend on the sulphite concentration. Dewaal's [44] measurements made with different oxygen partial pressures showed that the absorption rate of oxygen concentration to the power 1.5 suggested a second order reaction in oxygen. 38 Lineket al. [46] and others [47,48] measured oxygen absorption rates at several oxygen pressures (<2(105) N/m2) in approximately the same range of CCo2+,T,pH andC 5 Q 2- as Dewaal. They arrived at the reaction orders of n=0, q= 1 and m= 1 for oxygen partial pressures above 10s N/m2 or latm. An order of m=2 was realised at partial pressures of oxygen below 1 atm. Under similar experimental conditions, Srivastava et al. [42] concluded an order m=\ and variable orders with respect to sulphite and the promoting effect of cobaltous catalyst was proportional to its concentration. Observations made by Schultz et al. [34] suggested that the absorption rate of oxygen in aqueous sulphite solution is at least pseudo first order with respect to the dissolved oxygen. The rate of absorption was found to be independent of the sulphite concentration (w=0) above 10"2 M. Disagreement in kinetic constants obtained by the various authors under identical conditions, may be attributed to the difference in the oxygen solubility values adopted by the authors, or in the evaluation of kinetic constants from experimentally determined oxygen absorption rates. The following correlation reported in the literature [49,50] involving the influence of temperature (15-35°C) and concentration of solution (0-1M Na2S04) has been developed for the calculation of the solubility of oxygen. The solubility of oxygen cannot be determined directly in sulphite solution; however, it is possible in sulphate solution. It has been assumed that the solubility of oxygen in sulphate solution is equal to that in sulphite solution at the same concentration and temperature [46]. The kinetic equation derived from the data for hypothetical sulphite (no impurities) is given (2.39) by, 39 6010 k, = 10*(28.776/?// -204.3rCCoSO4exp 20.512 — - (2.40) The kinetic constant klt depends on both the kind and concentration of the sulphite used [46]. This is why the authors do not recommend taking up the rate data of the reaction from the literature. Copper and cobalt have been the most commonly used catalysts in aeration studies, but cobalt is known to be a more active catalyst than copper and is also less sensitive to impurities [43,51]. Ammonium and potassium sulphites are less frequently used than the sodium sulphite; however, the oxidation rates of K2S03 and Na2S03 are comparable while that of (NH4)^03 is slower [10,52,53,54]. The reason is that, in the presence of ammonia the less stable C o 3 + ions will be converted to less catalytically active [Co(NH3)6]3+ ions whilst in ammonia-free solutions a more hydrated cobalt species will be formed which catalyses the oxidation of sodium sulphite at a faster rate. The reaction rate has been found to be independent of copper concentration above 10"3 Molar and the cobalt concentration above lppm [34,52]. The pH value of sulphite solution decreases when it is oxidised to sulphate and has been found to have a negligible influence on the rate [46]. 2.5.2 Recent studies on oxygen mass transfer Some recent investigations on gas-liquid mass transfer of oxygen in aqueous sodium sulphite solution have been done by DeGraaf and Swiniarski [5,55]; however, Swiniarski's thesis has not been completed. Their works were mostly focused on the optimal production of secondary bubbles with the aim of determining the gas pumping characteristics as function of impellers (size, type, speed), baffles, impeller power consumption and tank geometry. DeGraaf [5] employed the sodium-sulphite oxidation method for the determination of oxygen mass transfer rates. A mixing model tank representing the first stage of the industrial 40 autoclave was used in this work. Experimental runs were performed at 82 % of capacity in a 2116 liter tank. Studies were done on three types of commercially available impellers (i) 45° pitched-blade turbine (axial flow), (ii) vertical-blade open turbine (radial flow) and (iii) disc turbine (radial flow). Impeller diameters and impeller depth of immersion were varied. The energy balance equation (2.15) was used to predict the critical agitation rate for the results obtain by DeGraaf for the three impeller types. The experimental estimates of the critical tip speeds for the 6-bladed disc turbine were found to be in good agreement with the theoretical critical tip speeds. The other two impellers showed a pronounced deviation from the theoretical critical tip speeds. This is likely due to the reduced conversion of momentum to bubbles in the absence of a disc, as well as to higher viscous losses of momentum. Furthermore, since the only variable in equation (2.15) is the depth of immersion, the other effects such as tank geometry or baffle configurations may be significant in deterrnining the precise critical agitation speed. Observation of impeller diameters has revealed that the greater the radial vector component in an impeller, the more effective it is at increasing the gas-liquid interfacial area and consequently the rate of oxygen mass transfer. Measurements were also made on the relationship between oxygen mass transfer, gas pumping rate and agitation power consumption at different impeller speeds. It was shown experimentally that scale-up on the basis of power input per unit volume is very unwise since impeller power curves change markedly as gas pumping becomes important. That is, slurry density rapidly decreases thus reducing the impeller power consumption, as the impeller becomes shrouded in gas. Beyond the critical agitation speed, the relationship between oxygen mass transfer and the total gas pumping rate in the system was found to be approximately linear. 41 Short and full-length baffles were also considered in the study. Improvements in the impeller power draw and the relative mass transfer efficiency were observed for short length baffles as compared to full-length baffles. Swiniarski [55] studied oxygen mass transfer from air in a vertically positioned 200 liter cylindrical vessel with a hemispherical bottom. The vessel and the table/thrust set-up was appropriately designed to take power measurements. The classical technique of sodium sulphite oxidation in the presence of a cobalt catalyst was used to measure gas-liquid mass transfer rates. Although this study has not been completely reported, available data from the experimental study showed rather low oxygen transfer rates with runs conducted without baffles. When full length baffles were installed, the mass transfer rates increased dramatically by a factor of three. However, these baffles increased the power consumption 7 times that of the unbaffled case. Therefore, the unbaffled tank was more energy efficient in dispersing gas. The oxygen mass transfer rate was also found to decrease as the agitator depth is increased for both the baffled and unbaffled case as expected from the previous energy balance. Private discussion with Peters [56] indicated that the unbaffled system is comparable to an impeller placed in an ocean, where there is no interaction from vessel walls to affect impeller motion. Swiniarski's unbaffled tank would be poor for liquid mixing, due to its cylindrical, vertical position and rounded bottom nature. Swiniarski observed that the presence of baffles increases the mass transfer rate markedly over the unbaffled case; but the mass transfer to energy ratio is better for the unbaffled case than for the baffled case. These observations might conclude that under conditions where oxygen mass transfer rates are much more important than energy costs, a baffled tank will give maximum utility. However, if energy costs are more important than oxygen mass transfer rates, then unbaffled tanks should be considered. 42 CHAPTER 3 EXPERIMENTAL 3.1 Apparatus A physical model representing the first stage of the industrial autoclave employed in the study is shown in Figure 12. The model was constructed from a half-inch thick transparent plastic material with a curved end. The inside dimensions of the tank shown in this figure are about five and half times smaller than that of the industrial autoclave (first compartment) used by Cominco, Ltd., for the zinc pressure leaching. Baffles of 10cm width were placed at a 25cm distance from the main agitator shaft at either end of the tank. The main agitator shaft was designed to take on different sizes and types of impellers. Therefore, it was possible to change impellers from the shaft without actually removing the entire work frame. Three types of impellers employed in this study include, (i) 4-bladed axial flow pitched-up impeller; (ii) 4-bladed axial flow pitched-down impeller;4 and (iii) 6-bladed radial disc impeller. The dimensions of the above-mentioned impellers are shown in Figure 13. A detailed diagram of the experimental set up is shown in Figure 14. A 1-hp motor was used to drive the main impeller shaft. An extended range of agitation rates was made possible by varying sizes and arrangements of the pulleys. 4 Pumping direction of an axial impeller is either down or up depending on the pitched blades and the direction of rotation. A pitched-down impeller thrusts the liquid downwards, while a pitched-up impeller thrusts the liquid upwards. 43 0 12.5mm Baffle ^ Splash guard Motor 1 HP -LX Baffle 25cm T 46cm 60cm 75cm 90cm Figure 12 A sectional view of the mixing model A digital pistol grip phototachometer (N-08210 series) was used in measuring directly the speed in rpm delivered by the impeller agitation. The torque imparted to the tank by the agitator motion was monitored by a tensile load cell C (mod-970-21 series 459) connected to the tank by a lever arm. The tank was mounted on a thrust bearing so that it can rotate freely. By Newton's third law, the reaction to the action produced by the tank during liquid agitation was taken by the load cell whose signal was recorded via a data logger. Other parameters monitored were the dissolved oxygen levels and the temperature of the tank contents. An oxygen probe was mounted in the tank to measure the percentage saturation of dissolved oxygen. Temperature measurements were taken by a thermocouple (type E) and the data were recorded directly in degrees Celcius. With the exception of the thermocouple, signals from the probe and the tensile load cell were recorded in millivolts. 44 4-Bladed Axial Impeller T w I same Da=23cm, W=3cm Curved-down 6-Bladed Radial Disc Impeller T Small | q=i8cm,d=7cm,W=5cm, L=4cm Medium | Da=23cm, d=9cm, W=6cm, L=5cm Large | D 28cm, d=11cm, W=7.5cm, L=5.5cm Figure 13 Impeller types and dimensions used Their respective engineering units were obtained from calibration curves. An IBM personal computer equipped with a data acquisition board PCB 00819/Rev C was used in acquiring data continuously from the experimental runs. 45 Motor 1HP Dissolved oxygen meter Dissolved oxygen probe -Splash guard Plastic "Tank Thermocouple E ' / l m P e l l e r -^Sand Turn-table Metal Support Figure 14 A detailed diagram of the experimental set-up. 3.2 Experimental procedure The reaction between sulphite and dissolved oxygen to form sulphate was used to determine the rate of oxygen mas s transfer and the sampling of the unreacted sulphite solution was carried out at time intervals according to the prevailing agitation rate and depth of 46 impeller immersion. A catalyst concentration of 5ppm (Coz+)was u s e d bi all the test runs. Standard iodometric titration of the unreacted sulphite was employed to determine the amount of oxygen absorbed during aeration. The tank was carefully cleaned before each run to get rid of any greasy material that might affect the value of the interfacial area which is proportional to the oxygen absorption rate. The volume of the mixing model tank is 250 liters at 100% capacity but tests were carried out at 80% capacity which demanded a liquid volume of 200 liters. The tests were carried out by first filling the tank up to the 200 liter mark with tap water. The calibrated thermocouple and dissolved oxygen measuring probe were mounted in the tank. Following the dissolution of the cobalt catalyst a 500 g measured amount of Na2S03 was added. To ensure a uniform mixture before initial sampling, the agitator was run at a very low speed and repeatedly stopped and restarted in order not to create any gas bubbles which might initiate any unwanted reaction. This was continued until the dissolved oxygen meter read less than 0.4%. After taking the sample at a time assigned to zero, tests were run at the desired agitation rates. The decrease in sulphite concentration was monitored by sampling the bulk solution at reasonable time intervals until the steady dissolved oxygen meter read greater than 0.4% saturation. The splash guard was needed to prevent loss of solution through the top of the mixing model due to splashing. For all the test samples, 25cc of solution was pipetted into a measured excess iodine solution with constant stirring. This was done by introducing the sample directly into the iodine solution with the pipette tip just below the liquid surface to prevent air oxidation to sulphate during transfer. At least 10 minutes were allowed to elapse before titration to ensure complete oxidation of sulphite to sulphate by the iodine. The residual iodine was then titrated with standard thiosulphate solution. Details of the sulphite determination are given in the literature [57,58]. 47 The bulk concentration of dissolved oxygen in the liquid was found to be very low (< 0.4 % sat. ~ 0.2 ppm) in multiple locations through the tank, as measured by the dissolved oxygen probe. The chemical analysis for dissolved oxygen confirmed this observation. The stoichiometry of the reaction shown in equation (3.1), indicates that 2 moles of sodium sulphite react with 1 mole of oxygen, and therefore, the absorption rate of oxygen is given by half the rate of sulphite depletion. This is interpreted by the relation (3.2). 2Na2S03 + 02^> 2A/a2S<94 (3.1) idSO2- 3 Rn = - - — - — mole Im -min (3.2) dSOl~ where —^— is the slope of the sulphite concentration against time. The oxidation of sulphite was found to be zero order in sulphite as seen in Figure 15 and assumed to be first order in oxygen. If the reaction is treated as slow (0.02<Ha<0.3), the overall liquid phase mass transfer parameter can be calculated from the following expression if C^, solubility of oxygen is known. Ro * , = M , « = 7 T (min"1) (3.3) During the test run the value C*0i was determined by employing a method originated by Winkler in 1888 [59,60]. After complete depletion of sulphite in the bulk solution, liquid aeration by the impeller was continued until the dissolved oxygen meter read 100% saturation. A sample was then taken for dissolved oxygen analysis. Manganese (II) sulphate was added first, followed by strong alkali, resulting in dispersed manganese (II) hydroxide 48 precipitates. The precipitates were rapidly oxidized by dissolved oxygen to hydroxides of higher valency states. On acidification in the presence of iodide ions, the oxidized manganese readily reverted back to the divalent state with liberation of triiodide ion equivalent to the original dissolved oxygen which is expressed in terms of mg/1. 02 + 6r + 4H+ = 2i;+2H20 (3.4) The sulphite method was first employed as an indication of bubble surface area and hence of the effectiveness of gas dispersion in agitated gas-liquid contactors. This method catalyzed by Co 2 + is well known to be oxygen mass transfer limited at the gas-liquid interface and the volumetric rate of oxygen absorption is directly proportional to the gas-liquid interfacial area [11,61]. 0.025 II8/mo; 0 .021 r u E r { 0.015 -te com Q. V) 0.01 -E 0 .005 0 ( i r i ^8 5 10 15 Time (min) 20 Figure 15 A typical rate curve for the oxidation of sodium sulphite. 49 CHAPTER 4 RESULTS AND DISCUSSION 4.1 Experimental Results The reproducibility of the experimental measurements was determined by triplicate runs performed on different days. The results as indicated in Figures 16 and 17 show good agreement. The results shown in Table 4.1 give an estimate of the experimental error within 95% confidence interval associated with the determination of the individual responses. 4.1.1 Unbaffled Tank Systems 4.1.1.1 Varying speed at constant impeller depth Oxygen mass transfer rates (mole/m3-rnin) were measured against change in the agitation rates for a single 6-bladed 23-cm radial disc impeller at a constant depth of 31.5 cm below the static liquid surface. The overall mass transfer parameter, Kg5, was obtained from a knowledge of the corresponding rates and oxygen solubility values as given in equation (3.3). The oxygen mass transfer rate and Kg were found to be sensitive to the hydrodynamics of the system. 5 The mass transfer parameter "Kg" combines the mass transfer coefficient k, and the interfacial area, i.e. Kg = 50 1.4 E CO E o E 1.2 2 0.8 tn tn to E c <D O) >, X O 0.6 0.4 (D % 0.2 rr Radial Impeller Imp. size = 23cm Op. depth = 16.5cm Baffled Tank +• Experiment 1 * Experiment 2 A Experiment 3 2 3 Impeller tip speed (m/s) Figure 16 E d (0 Q. W c a) 75 1 3 -ID a Radial Impeller Imp. size = 23cm Op. depth = 16.5cm Baffled Tank a EXPERIMENT 1 * EXPERIMENT 2 A EXPERIMENT 3 0 1 2 3 Impeller Tip speed (m/s) Figure 17 Plots showing the reproducibility of experimental results 51 Table 4.1 Error bar estimates RESPONSE ERROR BAR (mean ± estimated error) at diff. RPM (m/s) 180 (2.17) 240 (2.89) 300 (3.61) 360 (4.34) Rate (inolelnf-min) 0.1078 ±0.0015 ± 1.4 % 0.2205 ±0.0404 ± 1 8 % 0.6814 ±0.048 ± 7 % 0.9692 ±0.0551 ± 6 % (min') 0.36 ± 0.03 ± 8 % 0.71 ±0.10 ± 1 4 % 2.30 ±0.16 ± 7 % 3.04 ±0.10 ± 3 % Power (wutts) 110.81 ±0.64 ± 0.58 % 167.81 ± 13.94 ± 8 % 263.50 ±6.15 ± 2.3 % 461.75 ±52.01 ± 11 % Mass/Energy Ratio kgOJkW-h 0.3736 ±0.004 ± 1.1 % 0.5056 ±0.1313 ± 2 6 % 0.9933 ± 0.0905 ± 9 % 0.8077 ±0.1383 ± 1 7 % Error bars were based on three experiments performed on different days at each impeller tip speed. 52 The effect of impeller tip speed in the range of 0.72 ~ 5.06 m/s was studied and is depicted in Figures 18 and 19. In the range 2.17 ~ 5.06 m/s, increasing impeller tip speed resulted in greatly increased oxygen mass transfer rate. When the impeller tip speed reached 2.17 m/s, slight vortexing andrippling, being signs of markedly increased surface turbulence, were noticed visually. These data show that there is a strong dependance of oxygen mass transfer on the impeller tip speed. This is because an increase in impeller tip speed increases the intensity of turbulence and consequently the gas hold up. Also the gas is dispersed in the liquid in the form of smaller bubbles to present a larger interfacial area between the gas and liquid phases, at higher tip speeds. Mixing theory suggests that power response of a given impeller measured at various speeds in water should vary as N3D* or the tip speed cubed, (NDaf, at constant impeller diameter. Equation (2.24) shows this classical relationship between power and impeller tip speed. This relationship was examined for the gas-liquid system utilizing experimental data beyond the critical tip speed. At constant impeller diameter, the slope of the plot, Figure 20, was found to be 2.34, which indicates that the impeller power consumption increased at a rate less than predicted by equation (2.24). This shows that the mean density, p, (in the agitator envelope) of liquid plus gas is varying beyond the critical tip speed. 53 c 'E CO E j33 o E co" c CO w tn CO x O O CD -t—< CO CC 1.4 1.2 Impeller: Radial Impeller size : 23 cm critical depth : 46 cm Opt. depth : 31.5 cm Unbaffled tank TTS = 2.49 m/s ETS = 2.52 m/s 2 Ere 3 4 IMPELLER TIP SPEED (m/s) Figure 18 Effect of impeller tip speed on the rate of oxygen mass transfer. 4 03 0-co c to (0 0) CO Impeller type : Radial Impeller size : 23 cm critical depth : 46 cm Opt. depth : 31.5 cm Unbaffled tank TTS = 2.49 m/s ETS = 2.53 m/s 0 1 2 E T S 3 4 5 Impeller Tip Speed (m/s) Figure 19 Effect of impeller tip speed on the overall mass transfer parameter. 54 o q - Int = 1.34 Radial impeller Unbaffled tank Imp. size = 23 cm Opt. depth = 31.5 cm 0.1 0.2 0.3 0.4 0.5 Log(Tip speed) 0.6 0.7 0.8 Figure 20 A plot showing the relationship between power consumption and impeller tip speed. 55 4.1.1.2 Effect of depth of impeller immersion A cross-sectional view showing the five different impeller positions in the mixing model is provided in Figure 21. Figure 21 Impeller positioning in mixing model Radial Impeller : Figure 22 demonstrates the effect of depth of impeller immersion on Kg at constant impeller tip speeds. A range of five different impeller depths with 5 cm intervals, as shown in Figure 21, was studied with a 6-bladed 23-cm radial disc impeller. At a tip speed of 1.45 m/s or lower, the Kg values appear to be extremely low and independent of the impeller depth as compared to the other tip speeds. This is most probably due to the absence of agitator generated gas-liquid interfacial area. Visual observations made during such impeller speeds (0.72 ~ 1.45 m/s) revealed an almost undisturbed liquid surface. Impeller gas pumping was virtually absent, although liquid mixing was accomplished. 56 A -i o 5 -Impeller type Impeller size • critical depth • No baffles Radial > 23cm 46cm Impeller speed : X rpm=360 (4.34m/s) • rpm-318(3.83m/s) • rpm=272 (3-28^5) •f- rpm=240 (2.89rrvs) • rpm=120(1.45m/s) • rpm=60 (0.72m/s) . Kg (mir 4 -rail Mass Trans. Para 3 -2 -\ CD > o 1 -• m • • o H ( 1 ) I I I I 10 20 i 30 < I 40 Impeller Depth of Immersion (cm) Figure 22 Effect of impeller depth on the overall mass transfer parameter at constant tip speeds. Increasing the tip speed within the range of 2.89 ~ 4.34 m/s, resulted in a significant improvement in the Kg. There is a noticeable decrease in Kg with increasing impeller depth. Maximum values of Kg were noted at 11.5 cm impeller depth at these tip speeds. This is because it takes less energy to create a bubble at a shallow impeller depth. Figure 23 illustrates a plot of Kg against impeller tip speed at constant impeller depths. As expected, Kg increased with decreased depth and increased tip speed. Up to 1.45 m/s, no significant measurement in Kg was made in any of the five impeller depths studied. It is therefore obvious from the diagram that there exists a critical tip speed between 1.45 m/s and 2.89 m/s, depending on the impeller depth, where continuous bubble formation starts within the impeller envelope. 57 Tip Speed (m/s) Figure 23 Effect of tip speed on the overall mass transfer parameter at constant depths Points marked with letters A ~ E on the tip speed axis represent the theoretical critical tip speed values obtained from the energy balance equation (2.15) for the individual depths. Theoretically, the critical speed is defined to be the speed at which gas bubbles start to form at the impeller tip. A linear regression analysis was performed on the results above the theoretical critical tip speeds with the view of determining the experimental critical tip speeds. These were obtained by extrapolating the regression lines (shown as broken) to the tip speed axis. The theoretical (TTS) and the experimental (ETS) critical tip speeds values are presented in Table 4.2. Comparison of the results shown in this table depicts fairly good correlation with an impeller efficiency factor of 0.924. 58 Table 4.2 Comparison of theoretical critical tip speeds with experimental estimates (unbaffled case) for the 6-bladed radial disc impeller Impeller depth of immersion //(cm) CRITICAL TIP SPEED v* = — mis a Theo. critical tip speed= ^2gh EXPERIMENTAL ESTIMATES 23-cm 6-Rad disc, unbaffled tank 11.5 1.5 1.54 a = 0.924 16.5 1.8 2.09 21.5 2.05 2.10 26.5 2.28 2.40 31.5 2.49 2.53 Measurements were made to ascertain the effect of speed and impeller depth on the impeller power consumption. The results of power consumption by the 6-bladed radial disc impeller against a range of impeller depth at constant tip speeds are reported in Figure 24. At each impeller tip speed the lowest power consumption level was observed at the lowest depth (11.5 cm). Impeller power consumption was found to increase with increasing tip speed and impeller depth. However, within the range of 16.5 cm ~ 26.5 cm the power is not significantly affected by increase in impeller depth. 59 -i 1 1 i 1 i i i 1 0 10 20 30 40 Impeller Depth (cm) Figure 24 Effect of impeller depth on power consumption at constant speeds The power consumed by this impeller at 1.45 m/s or lower, compared to the other tip speeds, was found to be almost constant over the entire range of impeller depths studied. Theoretical equations indicate that energy consumption should vary with the density of the fluid being mixed, and this would indicate that the average density of fluid/gas mixture in the impeller zone is nearly constant. The measure of the ratio of the oxygen mass transfer rate (mole/m3-min) to the volumetric power consumption of the agitator (watt/m3) is termed the mass/energy ratio (kg oxygen/Kw-h). This indicates the effective use of energy by impellers to produce gas-liquid mass transfer of oxygen. Figure 25 shows that for the range of depths studied, 11.5 cm impeller depth, the lowest depth studied, gave better use of energy in enhancing oxygen mass transfer. 60 Figure 25 Effect of impeller depth on the mass/energy ratio at constant speeds. Axial (pitched-up) Impeller: Similar runs were conducted for a 4-bladed 23cm pitched-up axial impeller (45° pitched blade) under the same conditions used for the 23-cm diameter radial impeller. Figure 26 shows the effect of impeller depth on the overall mass transfer parameter at constant impeller tip speeds. This figure displays trends similar to Figure 22. The values of Kg plotted against tip speed at constant impeller depths are shown in Figure 27. The values of Kg produced by the axial pitched-up impeller appeared to increase markedly to placements of the impeller at depths of 21.5 cm to 11.5 cm. The estimates of the experimental critical tip speeds obtained from this figure are compared to the theoretical values in Table 4.3. The results as shown depict a poor correlation with theoretical critical tip speed. 61 I 4 cg 3 0-<n c (0 2 -(A CS 2 2 1 s o Pitched-up Axial imp. Imp. size = 23 cm critical depth = 46 cm Unbaffled tank Imp. speed — A — rpm = 375 (4.52 m/s) —t— rpm = 328 (3.95 m/s) - A — rpm = 277 (3.34 m/s) - » - rpm = 240 (2.89 m/s) 10 20 Impeller Depth of Immersion (cm) Figure 26 Effect of depth of impeller immersion on the overall mass transfer parameter at constant impeller speeds using an axial pitched-up impeller. Impeller Depth TSS sys • Depth=11.5cm 1.5 m/s A + Depth»16.5cm 1.8 m/s B 0 Depth-21.5cm 2.05 m/s c A Depth-26.5cm 2.28 m/s D x Depth=31.5cm 2.49 m/s E CL ai c CO 5 CD Pitched-up Axial impeller Impeller size • 23cm Unbaffled tank critical depth « 46cm 2 4 Impeller Tip Speed (m/s) Figure 27 Effect of impeller tip speed on the overall mass transfer parameter at various impeller depths using an axial pitched-up impeller 62 Table 4.3 Comparison of theoretical and experimental critical tip speeds for a pitched-up axial impeller (unbaffled case) Impeller depth of immersion H (cm) CRITICAL TIP SPEED v*=— mis a Theo. critical tip speed EXPT. ESTIMATES 23 cm Axial pitched-up. unbaffled tank 11.5 1.5 2.67 16.5 1.8 2.79 21.5 2.05 2.89 26.5 2.28 2.95 31.5 2.49 2.41 Figure 28 shows the effect of impeller depth on the power consumption at constant tip speeds. With the exception of the tip speed of 4.52 m/s, the power consumed by the impeller at various tip speeds was not greatly affected by an increase in the impeller depth. This is a result that would be expected if the impeller is not pumping much gas, and indicates that the main source of energy consumption is axial pumping of liquid. The results in Figure 29 show that lower impeller depths gave effective use of energy for producing gas-liquid mass transfer of oxygen. This observation is similar to that which was observed with the radial disc impeller. 63 300 250 -£ . 200 -c o Q. E 3 U) 150 -c cS 100 50 Pitched-up Axial imp. Imp. size = 23 cm critical depth = 46 cm Unbaffled tank Impeller speed: 4- rpm=375 (4.52 m/s) X rpm=328 (3.95 m/s) A rpm=277 (3.34 m/s) B rpm=240 (2.89 m/s) 10 20 Impeller Depth (cm) 30 40 Figure 28 Effect of impeller depth on the power consumption at various tip speeds using an axial pitched-up impeller. 5 -4 -CO EC >. 2> <B C UJ 2 -Pitched-up Axial imp. Imp. size = 23 cm critical depth = 46 cm Unbaffled tank Impeller speed : * rpm=375 (4.53 m/s) x rpm=328 (3.95 m/s) A rpm=277 (3.34 m/s) + rpm=240 (2.89 m/s) 10 20 30 40 Impeller Depth (cm) Figure 29 Effect of impeller depth on the mass/energy ratio at various tip speeds using an axial pitched-up impeller. 64 4.1.2 Baffled Tank Systems 4.1.2.1 Effect of Impeller Type The performance of the following types of impellers was investigated for a range of impeller tip speeds at a constant immersion depth of 11.5 cm: (i) 6-flat-bladed disc turbine, (ii) 4-bladed pitched-up axial flow turbine, (iii) 4-bladed pitched-down axial flow turbine. Figure 30 compares the various types of impellers mentioned above. It can be observed that the 6-flat-bladed disc turbine was more effective for promoting gas-liquid mass transfer and was found to have a better correlation with the theoretical critical tip speed. Both pitched-up and pitched-down axial impellers showed very poor correlation with the theoretical critical tip speed. Further, the axial pitched-up impeller gave much higher values of Kg (above ETS) than the pitched-down impeller. A comparison of the power consumption of each impeller at various impeller tip speeds is given in Table 4.4. This table reveals that a 6-flat-bladed disc impeller consumes more power than the other two impellers. However, it is more efficient in gas pumping, utilizing most of its energy to enhance oxygen mass transfer. 4.1.2.2 Effect of Impeller Depth A series of experiments was performed to study the influence of impeller immersion depth on the oxygen mass transfer using three different 6-flat-bladed disc impellers with diameters of 18 cm, 23 cm and 28 cm. With the exception of the 23-cm medium impeller, which was studied at three depths of 11.5 cm, 16.5 cm and 21.5 cm, experiments with the other two impellers were performed only at depths of 11.5 cm and 21.5 cm. The results for the various impeller sizes are shown in Figures 31, 32 and 33. 65 2 5 Impeller Type ETS Opt. depth = 11.5cm x Radial (six bladed) 1.53 m/s TTS = 1.5 m/s H Axial pltched-up 2.65 m/s Imp. size = 23cm A Axial pitched-down 2.35 m/s Baffled tank - / / A / s - / s • T T S / / . _ A — — i i./ I 0 1 2 3 4 5 Impeller Tip Speed (m/s) Figure 30 Effect of impeller type on the overall mass transfer parameter. Table 4.4 Effect of impeller type on the impeller power consumption Impeller Impeller Power Consumption Tip speed 4-Bladed axial pitched-down 23 cm 4-Bladed axial pitched-up 23 cm 6-Bladed radial disc 23 cm m/s watts V.P. kg/kwh watts V.P. kg/kwh watts V.P. kg/kwh 2.89 34.4 .172 .615 38.1 .191 2.231 57.6 .288 5.5 3.52 70.7 .354 .923 77.9 .39 2.885 94.6 .473 6.538 4.34 128.8 .644 .692 129.7 .649 3.769 188.4 .942 3.946 Operating impeller depth = 11.5 cm kg/kwh = Mass/energy ratio V.P. = Volumetric power kW/m3 66 Figure 31 Effect of impeller depth on the overall mass transfer parameter for radial 18-cm impeller. The points marked with letters A, B and C represent the theoretical critical tip speeds and their respective values are indicated on the diagrams. The experimental critical tip speeds were estimated as previously discussed. These figures show that the values of Kg are very sensitive to lower impeller depths. Also there are strong indications that the critical tip speeds increase with increasing impeller depth. Table 4.5 compares the results of the impeller power draw at different impeller depths shown. The power draw was greatly affected by the depth of impeller immersion. The power increased markedly with depth in all the three impeller sizes studied. 67 fl) « CL co c CO to I CD > O 8 7 h 6 5 h 4 3 2 h 1 0 Impeller Depth Sym ITS ETS ta Depth = 11.5cm A 1.5 m/s 1.53 m/s +• Depth = 16.5cm B 1.8 m/s 2.05 m/s x Depth = 21.5cm C 2.05 m/s 2.14 m/s Radial Impeller Imp. size = 23cm Baffled tank 2 3 Impeller Tip Speed (m/s) Figure 32 Effect of impeller depth on the overall mass transfer parameter for radial 23-cm impeller. 5£ CO a. 0) > O Radial Impeller Imp. size = 28 cm Baffled tank ETS Depth = 11.5cm A 1.5 m/s 1.52 m/s A Depth = 21.5cm B 2.05 m/s 2.08 m/s 2 3 4 Impeller Tip Speed (m/s) Figure 33 Effect of impeller depth on the overall mass transfer parameter for radial 28-cm impeller. 68 Table 4.5 Effect of impeller depth on the impeller power consumption 6-Bladed Depth of Impeller Immersion Radial disc 11.5 cm 16.5 cm 21.5 cm Impeller watts V.P. watts V.R watts V.P. size kW/m3 kW/m3 kW/m3 Rad-18 cm 59.0 .295 229.0 1.145 Rad-23 cm 92.6 .463 246.0 1.23 345.0 1.725 Rad-28 cm 170.7 .854 538.2 2.691 Impeller Tip Speed = 3.5 m/s V.P. = Volumetric Power 4.1.2.3 Effect of Diameter The effect of impeller diameter on Kg was investigated at a constant depth of 11.5 cm. The diameters of the impellers employed were 18 cm, 23 cm and 28 cm. Figure 34 shows that an increase in impeller diameter increases the value of Kg. This figure also suggests that as the distance from the impeller to the baffles and the tank walls decreases the relationship between Kg and the impeller tip speed displays varied and complex trends. It is conclusive from these results that larger impellers and the presence of baffles interfere with the meaning of "tip speed". This is because baffles reflect eddies back to the agitator which can either add to or subtract from the tip speed in a "stationary" medium. 69 Also eddies are less severe for small agitators because they are further from the tank corners and walls as well as baffles. It was observed that the smallest impeller gave the poorest gas distribution whereas the larger ones gave extensive gas bubble dispersion within the system. It is also apparent from this figure that at a tip speed of about 3.8 m/s to 4.34 m/s the 23-cm diameter radial impeller is marginally the most efficient for enhancing oxygen mas s transfer. Table 4.6 sums up the effect of impeller diameter on the impeller power consumption and the volumetric power at constant depth of immersion. The impeller power consumption measurements were found to increase at a much lower rate than predicted by the energy equation (2.25). Analysis of the results showed that impeller power draw varied as tip speed to the power 1.2,2.3 and 2.5 at constant diameters of 18 cm, 23 cm and 28 cm respectively. In mixing theory, the relationship between power draw and impeller diameter is given by Power°cD2 at constant tip speed (as predicted by equation (2.24)). This is established with different diameter impellers of the same design which are run in water in proportionally larger tanks (i.e. impeller to tank diameter remains constant). Although, only one tank diameter was employed in this work, the relationship was verified with the power measurements obtained in this study. Analysis of the results at constant tip speed disclosed that impeller power consumption increased at a rate less than predicted. The cause for this observation may be due to decrease in the effective density of liquid plus gas in the impeller envelope that results from much gas pumping. As the impeller diameter increases there is a simultaneous increase in the impeller gas pumping rate which may exceed the increase in the liquid pumping rate and thereby increase the gas-liquid ratio. If this is so, the impeller power draw should tend to decrease with decrease in density. 70 0 1 2 3 4 5 6 Impeller Tip Speed (m/s) Figure 34 Effect of radial disc impeller diameter on the overall mass transfer parameter Table 4.6 Effect of radial disc impeller diameter on the impeller power consumption Impeller Tip Speed m/s Radial Impeller Diameter (size) Rad- 18 cm Rad- 23 cm Ri id -28 cm watts V.P. watts V.P. We itt* V.P. 2.5 40.5 .203 .245 .424 48.9 84 •7 3.0 49.7 .249 66.5 .333 12 :H ) .6 3.5 59.0 .295 92.6 .463 17 0" 1 .854 Impeller Depth = 11.5 cm V.P. = Volumetric power kW/m3 71 4.1.3 Comparison of Baffled and Unbaffled Tank systems The next set of experimental runs was carried out to examine the usefulness of baffles in tanks of this shape6. The results obtained with the use of baffles were compared with the results without baffles. Comparisons were made at three different impeller depths of 11.5 cm, 16.5 cm and 21.5cm, using pitched-up axial impellers and three 6-bladed radial disc impellers of different sizes. 4.1.3.1 Impeller depth at 11.5 cm The effect of a baffled tank, using the 4-bladed 23-cm pitched-up axial impeller on the Kg> is illustrated in Figure 35(a). This figure indicates no significant improvement in Kg when baffles are employed with this type of impeller. This indicates an absence of interaction between the impeller and the baffles and tank walls as a result of the nature of the flow pattern generated by this impeller. The relationship between Kg and the impeller tip speed shows a high degree of linearity within the range of tip speeds covered in the study. The amount of oxygen absorbed in kg per unit energy, as depicted in Figure 35(b), reveals that baffles are useful at some but not all tip speeds. Figures 36 (a) and (b) present the results of baffled and unbaffled tanks using the 18 cm diameter radial disc impeller. It can be seen from these figures that the introduction of baffles did not show any considerable improvement in the Kg with increasing speed. This is probably due to the low proximity of the impeller to the baffles and also to the boundaries of the tank. There is little interaction effect if the baffles and the boundaries of the tank are further away from the impeller. This impeller is clearly more efficient than the pitched-up axial impeller shown in Figure 35. 6 The shape is characterized by the first stage (i.e. the stage of highest gas consumption) in oxidative pressure leaching autoclaves. 72 Comparing the data presented in Figures 35(a) and 36(a), a high degree of linear relationship between Kg and impeller tip speed can be assumed where there is very little interaction between the impeller, baffle and tank wall. As shown in Figure 36(b), there is a slight improvement in the mass energy ratio with a baffled tank. The results shown in Figures 37(a) and 38(a) indicate that as the impeller gets closer to the baffles and tank walls, improvement in the value of Kg with a baffled tank becomes more significant at the lowest impeller depth of 11.5 cm. From Figures 37(b) and 38(b) it can be seen that the mass energy ratios are significantly improved with the use of baffles at this impeller depth. However, Figures 38(a) and (b) demonstrate that baffles are very important at tip speeds of up to about 4 m/s beyond which they ceased to enhance the oxygen mass transfer or Kg and also decreased the mass energy ratio. At tip speeds greater than 4 m/s, with the largest (28 cm) impeller, the unbaffled tank seems to be more effective. 4.1.3.2 Impeller depth at 16.5 cm and 21.5 cm An interesting observation in this work is that as the depth is increased, the use of baffles results in a pronounced decrease in Kg and a concomitant increase in the impeller power consumption, leading to a dramatic decrease in the mass energy ratio. The results are demonstrated in Figures 39,40 and 41. From these figures, the use of baffles appear to be unattractive at increased impeller depth beyond 11.5cm. 73 " 5 CT a > O 2 -Pitched-up Axial imp. Imp. size = 23cm Opt. depth = 11.5 cm TTS = 1.5 m/s ETS = 2.67 m/s 2 4 Impeller Tip Speed (m/s) rr S> V) cd 2 5 -4 -Pitched-up Axial imp. Imp. size = 23cm Opt. depth = 11.5cm Baffled tank Unbaffled tank (a) (b) Impeller Tip Speed (m/s) Figure 35 Effect of baffles using a 4-bladed 23-cm pitched-up axial impeller at 11.5-cm depth on the (a) Overall mass transfer parameter (b) Mass/energy ratio 74 § 3 CD 2 ra CL H co CO cd 5 1 S O o q> cs 2 <S 4 CC >. 2" 3 CD d c U J Radial Impeller Imp. size = 18cm Opt depth = 11.5cm TTS = 1.5m/s ETS = 1.8 m/s "1 J- Baffled tank ) Unbaffled tank TTS (a) ETS 2 3 Impeller Tip Speed (m/s) Radial Impeller Imp. size = 18cm Opt. depth = 11.5cm Battled tank Unbaffled tank (b) Tip speed (m/s) Figure 36 Effect of baffles using a 6-bladed radial 18-cm disc impeller at 11.5-cm depth on the (a) Overall mass transfer parameter (b) Mass/energy ratio 75 „ 6 E, CD CL & CO to 5 CD a .c o n rr Si LU •ft CO CO 2 5 4 3 2 1 H Impeller type : Radial Impeller size = 23cm Opt. depth = 11.5cm 8 7 6 -5 -4 3 2 1 0 ETS + Baffled tank : 1.53 m/s • Unbaffled tank : 1.54 m/s TTS -1.5 m/s TTS 2 Impeller Tip Speed (m/s) Radial Impeller Opt depth = 11.5cm Imp. size = 23cm Baffled tank Unbaffled tank (a) (b) Impeller Tip Speed (m/s) Figure 37 Effect of baffles using a 23-cm 6-bladed radial disc impeller at 11.5-cm depth on the (a) Overall mass transfer parameter (b) Mass/energy ratio 76 co r— V) •5 CD > O Radial Impeller Imp. size = 28cm Opt depth = 11.5cm ETS A. Baffled tank 1.52 m/s TTS-1.5nVs B Unbaffled tank 1.52 m/s (a) 2 3 4 Impeller Tip Speed (mis) -C o CD o 8 7 6 H 5 •2 4 CO DC 01 3 «5 2 -cn co 2 1 -Radial Impeller Imp. size = 28cm Opt. depth = 11.5cm Baffled tank Unbaffled tank (b) 0 2 4 6 Impeller Tip Speed (m/s) Figure 38 Effect of baffles using a 28-cm 6-bladed radial disc impeller at 11.5-cm depth on the (a) Overall mass transfer parameter (b) Mass/energy ratio 77 E, co <5 4.5 4 -3.5 -3 2.5 2 1.5 H 1 0.5 0 <u g rr >. 0) 1.5 1.4 1.3 1.2 -1.1 -1 -0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 Radial Impeller Imp. size = 23cm Opt. depth = 16.5cm crit. depth = 46cm TTS = 1.8 m/s ETS • Unbaffled tank : 2.09 nVs + Baffled tank : 2.05 nVs (a) Impeller Tip Speed (m/s) Radial Impeller Imp. size = 23cm Opt. depth = 16.5cm (b) 0 2 4 Impeller Tip speed (m/s) Figure 39 Effect of baffles using a 23-cm 6-bladed radial disc impeller at 16.5-cm depth on the (a) Overall mass transfer parameter (b) Mass/energy ratio 78 'E, ^ 3 cd k ra CL £ 2 in c CO co co co CD Radial Impeller Imp. size = 23cm Opt. depth = 21.5cm ETS H Unbaffled tank : 2.10 m/s x Baffled tank : 2.14 m/s "ITS = 2.05 m/s (a) 2 3 4 Impeller Tip speed (m/s) 1.4 I 1 2 1 0.8 CD CD >> X o O l o ra cr >. O ) o c UJ CO « 0.2 0.6 0.4 Radial Impeller Imp. size = 23cm Opt. depth = 21.5cm B Unbaffled tank x Baffled tank (b) 0 1 2 3 4 5 Impeller Tip Speed (m/s) Figure 40 Effect of baffles using a 23-cm 6-bladed radial disc impeller at 21.5-cm depth on the (a) Overall mass transfer parameter (b) Mass/energy ratio 79 Figure 41 Effect of baffles using a 28-cm 6-bladed radial disc impeller at 21.5-cm depth on the (a) Overall mass transfer parameter (b) Mass/energy ratio 80 Table 4.7 Comparison of the theoretical and experimental critical tip speeds for three different radial disc impellers in baffled and unbaffled tanks. Impeller CRITICAL TIP SPEED v 4 = " f (m/s) depth Theo. Experimental estimates for Radial disc Impeller H critical 18-cm 6-Radial 23-cm 6-Radial 28-cm 6-Radial (cm) tip speed Baffled Unbaff. Baffled Unbaff. Baffled Unbaff. 11.5 1.5 1.68 1.88 1.53 1.54 1.52 1.52 16.5 1.8 2.05 2.09 21.5 2.05 2.21 2.14 2.10 2.08 1.67 Table 4.7 presents an overall comparison of theoretical critical tip speed with its corresponding experimental critical tip speed estimates for both baffled and unbaffled tanks. The results show good correlation of theoretical with experimental critical tip speeds. 81 4.2 Discussion 4.2.1 Effect of Impeller Speed Recent work by DeGraaf established that beyond a critical tip speed the relationship between oxygen mass transfer rates and impeller tip speed is linear [5]. Therefore, his experimental critical tip speed values were obtained from the intersection of the linear portion of the curve with the tip speed axis. He also found that the oxygen mass transfer and the impeller gas pumping are linear functions of agitation rate with their critical tip speeds. approximately equal. For this reason equation (2.23) which predicts a proportionality between impeller gas pumping capacity and impeller tip speed can be used to support this linear regression method of estimating the experimental critical tip speed. Analysis of his results shows that the number of data points used in determining the critical tip speeds is often only three. These few data points, it must be argued, are insufficient to merit the excellent correlation of (X997 he obtained with equation (2.15) for the 6-bladed radial disc impellers. More experimental data points were incorporated in this work with a view of providing greater assurance of graphical linearity and also to assess the reliability of this procedure of deterrnining the critical tip speed. It can be observed from Figures 18 and 19 that at very low impeller speeds, improvement in the value of Kg is only marginal, and this reveals that impeller gas pumping is virtually absent below a certain critical speed marked TTS. Beyond this speed the value of Kg increases rapidly with increasing tip speed, and bubbles are observed to form at the impeller. The theoretical critical tip speed and the experimental critical tip speed were found to be in good agreement. 82 At high impeller speed the natural turbulent forces associated with the rotation of the radial disc impeller tend to break up bubbles and thereby increase the residence time of gas bubbles. On the other hand, at low impeller speeds any gas bubbles that have been generated by the impeller coalesce to the extent where the buoyancy forces remove bubbles rapidly. The basic energy equation relating power and tip speed states that the power draw of an impeller should increase proportionally with the cube of the tip speed (P«={A© f l}3). The measured impeller power consumptions were found to increase less than expected from the energy equation. This is because there is a significant variation (decrease) in mean density of the liquid plus gas due to impeller gas pumping. It should be noted that when impellers are rotated in tanks specifically without baffles the depth of vortex formed is a function of impeller speed. The vortex becomes deeper as the speed is increased until it reaches the impeller. At this point gas touches the impeller and may be drawn into the liquid. The power necessary to drive the impeller when gas and liquid are both in contact with it, is less than that required when in contact with liquid alone. 4.2.2 Effect of Impeller Depth Examination of the experimental data has shown that depth of impeller immersion is a very important process variable in this study. The results demonstrate that as the agitator was brought upward or as the height of the liquid above the impeller decreased, the value of Kg improved dramatically. The rapid increase in Kg may be due to increased suction capacity of the impeller at shallow depths. Also it takes less energy to create a bubble at i low depth as v* varies as h2. It was observed during experimental runs that the rate of vortex formation increased with decreased depth which is desirable for effective gas dispersion. The gas-liquid mass transfer of oxygen was maximized at a constant shallow depth of 11.5 cm for agitation rates of 2.89 m/s and above, as shown in Figure 22. / 83 It is clearly shown in Figure 23 that increasing tip speed increased Kg for all the depths studied. The trend of results illustrate that a maximum impeller speed is likely to be reached, depending on the depth, beyond which any further increase in speed will not have any significant change in Kg. For example, at 11.5 cm impeller depth, the optimum Kg is liable to be attained close to 4 m/s. A tendency for such a maximum speed to increase with increasing impeller depth is discernible from the diagram. Power draw measurements in Figure 24 show that minimum power draw is attained at shallow depth but increases rapidly with increase in impeller depth as well as impeller speed. This shows that the gas-liquid ratio being pumped by the impeller increases with decreasing depth. It can be inferred that the shallowest impeller depth used (11.5 cm) gives the most effective use of energy by impellers to produce useful gas-liquid mass transfer of oxygen. The results obtained with the pitched-up axial impeller firmly supports this inference. For purposes of gas dispersion and consequent enhancement of oxygen mass transfer, axial pumping impellers were generally found to be unsuitable especially with increasing impeller depth. The distinction between the mechanism of fluid mixing and the mechanism of gas dispersion can be demonstrated with Figures 22 and 24. At impeller speeds of 1.45 m/s and below, increasing depth had no noticeable effect on the Kg which is close to zero compared to the other tip speeds, and the free liquid surface was almost undisturbed. Though a few bubbles were occasionally seen during impeller mixing there was essentially no entrainment of gas bubbles. In their absence it could be assumed that the density of the liquid would be constant at these low agitation rates. In fluid mixing practice based on a single phase system, the impeller power consumption is expected to vary proportionally with the liquid density. That is, if the liquid 84 density is constant throughout a solution, the impeller power draw also remains constant. The corresponding power draw measurements for Figure 22 are shown in Figure 24. At the speed of 1.45 m/s, the power consumption was also found to be nearly constant with impeller depth which adds substantial support to the finding that mixing rather than gas dispersion is accomplished when the effective density is not affected by the presence of gas bubbles. On the other hand, as the agitation rate increases, especially at low impeller depth, Kg increases rapidly with a corresponding decrease in impeller power consumption. This is because the impeller tends to draw a substantial amount of gas into the liquid from the free liquid surface for the reaction to be enhanced. Due to entrained gas bubbles the effective liquid density declines. Hence, the density of the liquid cannot be assumed to be the same throughout the entire solution. The "unloading" of the impeller due to the presence of gas bubbles tends to decrease the impeller power consumption. This points to the fact that the optimum conditions for liquid mixing and for gas dispersion are quite different. 4.2.2.1 Critical Tip Speed A graphical technique was employed in the determination of the experimental critical tip speed. This critical speed was found as the intercept of linear regression line extrapolated to zero mass transfer. This technique was supported by the fact that impeller gas pumping varies proportionally with the tip speed as predicted by equation (2.24) and also by the finding that impeller gas pumping rates vary approximately linearly with the agitation rates, as did the oxygen mass transfer rates [5]. Besides this line of reasoning, a linear relation between mass transfer and tip speed is not predicted by any theory, but there is also no theory for any non-linear relationship. In the absence of a theory, and with an average of five experimental points, only a linear extrapolation to zero mass transfer rates is justified. A polynomial 85 regression curve through experimental points fits the data better, but provides no method of estimating the critical tip speed. However, a critical tip speed can be observed very clearly for there is a tip speed below which no bubbles can be observed. Table 4.2 shows good agreement of the theoretical critical tip speed values with the experimental estimates obtained with a 6-bladed radial disc impeller in an unbaffled tank. A plot of v* versus h2 evinced a fairly good correlation of 0.924 which adds substantial support to the concept that the critical tip speed is very sensitive to changes in impeller depth and that equation (2.15) is applicable. A very poor correlation was observed for the pitched-up axial impeller. Table 4.3 shows that the experimental critical tip speeds are far from the theoretical values. This is likely due to the kind of flow pattern generated by this type of impeller. Examination of Table 4.7 reveals that impeller depth is the most significant variable for determining the critical tip speed. The baffles and impeller diameter had no dramatic effect on the critical tip speed. Generally the estimates obtained for the experimental critical tip speeds correlated well with the theoretical critical tip speeds. Therefore, these results suggest that equation (2.15) which contains impeller depth as the only variable, is primarily a good concept. It can be observed from the results that in situations where eddy interactions are high, i.e. with larger impellers and baffled tanks, the relationship between Kg and the impeller tip speeds is complex. The linear extrapolated lines (broken) are regarded as the ideal trend between Kg and impeller tip speed when eddies are less severe. Therefore, it is reasonable to deduce that the presence of baffles and larger impellers interfere with the meaning of "tip speed". This is because baffles and tank corners reflect eddies back to the impeller, and 86 these can either add to or subtract from the absolute tip speed, depending on whether the reflected eddy is against the direction of the impeller or with it. Also eddies are more severe for large impellers because they are closer to the baffles as well as the tank corners. It is important to note that as impeller agitation increases, high velocity liquid streams are produced which move throughout the vessel. As these high velocity streams encounter stagnant or slower moving liquid, momentum transfer occurs. These momentum effects are altered by eddy reflections from the wall and baffles. These could add to or subtract from the momentum vectors originating from the impeller blades which will make the relative tip speed (between the impeller and the solution) different from the absolute tip speed (that assumes the solution is stagnant). Though equation (2.15) shows fairly good agreement with experimental results, it is fair to correct it for eddy interaction since this relation is based on the tip speed relative to the medium being mixed. Additional variables may have to be considered to predict accurately the theoretical critical tip speed apart from impeller depth as contained in equation (2.15). A more appropriate relation must include the influence of such variables as impeller proximity to tank boundaries, impeller type, viscous effects, tank geometry, baffle configuration and a description of the path by which gas is transferred from the plenum to the agitator tip. Visual observation during experimental runs could perhaps be an alternative for determining the experimental critical tip speed. To determine this, a variable speed motor to drive the impeller shaft may be used to establish the speed which will be the point at which the vortex reaches the impeller and there is a simultaneous dispersal of the bubbles throughout the tank. 87 In spite of the shortcomings of equation (2.15), it makes an appreciable contribution to an understanding of critical tip speed by establishing that it increases with increased impeller depth. 4.2.3 Effect of Impeller Type In view of the finding that baffles enhance oxygen mass transfer at the lowest measured impeller depth of 11.5 cm, the performance of the three impeller types were compared at this depth over a range of impeller speeds. The six-bladed radial disc impeller was found to be at least 2.8 times more effective than the upward pumping axial impeller for producing gas-liquid mass transfer of oxygen. This is probably due to the centrifugal action of the radial impeller which provides high fluid velocity within the system. High fluid velocity enhances the shear stress which is generally considered as a prerequisite for good gas dispersion and high oxygen mass transfer7. Also, the presence of the disc forces more gas to flow through the high shear zone at the tip of the impeller blades. By their nature, axial impellers direct their maximum flow parallel to the impeller shaft, the low shear zone, which results in low vortexing and consequent decrease in gas dispersion. The pitched-down axial impeller showed significant instabilities in the flow pattern and the gas bubbles were poorly dispersed. This is probably why the downward pumping axial impeller was found to be the worse choice for gassed systems. Therefore, for purposes of gas dispersion, impellers that exhibit minimum axial flow are desirable. Although the six-bladed radial disc turbine consumed more power than either of the other types of impellers, it was found to be the most energy efficient as measured by the 7 Increase in shear force means more interfacial area is produced for reaction 88 mass energy ratio (kg Oj/kw-h) within the impeller speeds covered in this study. This is shown in Table 4.4. The power consumed by the upward pumping axial impeller and that for the downward pumping axial impeller were fairly close. 4.2.4 Effect of Diameter The effect of impeller diameter examined at a constant depth of 11.5 cm, showed that an increase in impeller diameter resulted in dramatic rise in Kg values. This is due to an increase in the impeller gas pumping capacity as a result of larger circumferential and cross-sectional area swept out by the impeller. Also, large impellers create a large vortex which penetrates to the depth of the impeller and supplies more gas to be entrained in the solution that is being pumped by the impeller. It can be deduced from Figure 34 that at low impeller tip speeds larger impellers are desirable for producing high oxygen mass transfer. However, at very high speeds the importance of larger impellers seem to be diminished. The reason is that intense agitation with such impellers create excessive gas bubbles which flood the system. These bubbles because they are now closer to each other easily coalesce to form larger ones, thereby decreasing the effective interfacial area, and hence, the decrease in Kg. As the equation (2.15) suggests, a change in the impeller diameter showed no significant effect on the critical tip speed (Figure 34). However, as impeller diameter increases the critical tip speed further approaches the theoretical critical tip speed. The power draw measurements have shown that a slight increase in impeller diameter increased markedly the impeller power consumption. However, the impeller power consumption increased at a rate less than expected from the energy equation (P^D2 at constant tip speed). The cause of this fall in impeller power draw, as explained earlier, is a result of effective density decrease due to increased gas volume fraction associated with 89 impeller gas pumping. Although, larger impellers consume more energy, they greatly enhance oxygen mass transfer. Therefore if enhancement of oxygen mass transfer is much more important than energy cost, then according to this work the 28-cm diameter impeller would be more suitable below a tip speed of about 3.8 m/s. It is quite discernible from Figure 34 that above this tip speed the 23-cm diameter impeller is likely to perform better with respect to increased oxygen mass transfer and higher mass energy ratio. It can be inferred from the above that larger impellers would be the best choice for enhancing mass transfer at low tip speeds. 4.2.5 Effect of Baffles Tests done with baffles have demonstrated that they only improve the gas-liquid mass transfer of oxygen at shallow depths. The impeller power draw at 11.5 cm depth was lower in the presence of baffles than in the unbaffled tank. This is probably due to the presence of a high gas fraction in the impeller shear zones which also serves to explain the high Kg values that were observed. Generally, the mass of oxygen absorbed per unit net energy delivered to the liquid was found to be high at this level. Although, there was no significant change in Kg observed for 18-cm radial and the 23-cm axial impellers, the corresponding mass energy ratios for the baffled tank were slightly higher than that for the unbaffled tank. Figure 38 suggests that removal of baffles beyond a tip speed of about 4.0 m/s is beneficial when dealing with a 28-cm impeller diameter. A spectacular decrease in mass transfer and a rapid increase in impeller power consumption accompanies an increase in depth beyond 11.5 cm with a baffled tank. This is undoubtedly due to the higher energy needed to form bubbles at a greater depth and to the 90 absence of deep vortexes which limit the amount of gas draw into the solution by the impeller. The presence of baffles also changes the course of fluid flow with a resultant decrease in velocity. This effect promotes high energy losses. A relative improvement in mass transfer and a lower power consumption was realized in the unbaffled case. It is evident from Figures 39 ~ 41 that as the impeller depth increases the power saved using an unbaffled tank instead of a baffled tank becomes more substantial. The results obtained here confirm that while baffles promote fluid mixing, they interfere with gas pumping by agitators. 91 CHAPTER 5 SUMMARY, CONCLUSIONS AND RECOMMENDATIONS 5.1 Summary and Conclusions The tank shape that represents the first stage of most industrial autoclaves is vertically asymmetrical. The zinc pressure leach vessel at Cominco, Trail, is a typical example. The effect of this asymmetry has been studied relative to the work of Swiniarski (uncompleted thesis) who used a cylindrically symmetrical tank [55]. The measurements made in this study for the unbaffled asymmetrical tank shape are equivalent, in their effect, to a large amount of baffling in Swiniarski's symmetrical tank of the same volume. In the absence of baffles and under similar operating conditions (about 11.5 cm and 21.5 cm impeller depths with 23-cm and 28-cm 6-bladed radial disc impellers) the mass transfer rates obtained for the asymmetrical tank are at least 3.6 times higher than the symmetrical tank. The energy consumption is about 20 ~ 40 times higher than that of the syrnmetrical tank. When baffles were added to Swiniarski's tank and at the operating conditions stated above, the mass transfer and the impeller power consumption increased by factors of 3 and 7 respectively which are comparable to the unbaffled asymmetrical tank results. The symmetrical tank configuration has been found to give lower fluid forces than the asymmetrical tank configuration. These forces are affected by the proximity of the impeller to a particular asymmetrical feature in the tank (comers, baffles, etc.). Hence, the role of 92 the tank is determined by its interaction with an impeller. This interaction increases as the impeller tip gets closer to the walls of the tank. The limiting case is an impeller in the ocean where there is no interaction from vessel walls to affect impeller motion. From the foregoing, it is expected that a cylindrically symmetrical tank should have minimum interaction with the impeller, if it is without baffles. Baffles increase the interaction between the impeller and the tank walls, and in cylindrically symmetrical tanks, Swiniarski has shown that baffles increase both mass transfer rates and impeller energy consumption dramatically. However, since energy consumption outpaces mass transfer rates (under most conditions), baffles usually decrease mass energy ratios. Higher mass transfer rates with the unbaffled asymmetrical tank have indicated that corners and other asymmetric features within the tank increase the interaction with the impeller and make the system behave as if it has baffles. The advantages derived from the asymmetrical tank provides justification for the use of such tank geometry in Cominco's zinc pressure leaching. The following conclusions are made, based on the experimental measurements acquired with the first stage physical mixing model (asymmetrical tank): 1. Impeller tip speed increases Kg significantly beyond a certain critical speed. Below this speed Kg is almost zero. Kg will not increase infinitely with increasing tip speed. A maximum speed is evident beyond which Kg remains unchanged. 2. Impeller immersion depth, which has been ignored in chemical engineering theories, was found to be the most important parameter for determining the critical tip speed, effective gas dispersion and consequent mass transfer enhancement. The overall mass transfer parameter, Kg, is enhanced at shallow depths, with a corresponding high mass energy ratio. The Kg and the mass energy ratio decrease as the depth of impeller immersion 93 is increased for both baffled and unbaffled tanks. The critical tip speed increased with impeller immersion depth. Experimental results support the theoretical equation based on an energy balance between the potential energy of a bubble and the kinetic energy of an equal volume of liquid or slurry (v ,^, = (2gh)V2). Thus, the energy required to create a bubble increases as the impeller depth, h, is increased. Though this equation comes close to predicting the critical tip speeds for 6-bladed radial disc impellers, additional variables such as viscous effects, tank geometry, impeller type, impeller proximity to the tank wall, baffled configuration and a description of the path by which gas is transferred from the plenum to the agitator tip must be considered to develop a more accurate model. 3. The flat 6-bladed radial disc impeller is at least 2.8 times more efficient than the pitched-up axial impeller in terms of oxygen mass transfer. The least efficient was the pitched-down axial impeller. The radial impeller is also the most efficient impeller with respect to the mass energy ratio (kg oxygen/kW-h), even though its power consumption is the highest. Therefore, the best impellers for pumping gas into a solution and enhancing mass transfer are those that have very little axial flow through them. 4. Increasing the impeller diameter at constant impeller tip speeds increases oxygen mass transfer rates or Kg. Also, a larger impeller diameter increases the impeller power consumption at a rate lower than predicted by the energy equation. Impeller gas pumping is proportional to the circumferential area swept out by the impeller blade tips. The greater the radial vector component in an impeller, the more effective it is at increasing the gas liquid interfacial area. 5. Baffles added to the asymmetrical tank make the following differences: 94 (i) at low impeller depths of immersion, baffles increase both Kg and the mass/energy ratios. Again, at such depths and at low tip speeds just above the critical tip speed, baffles result in a significant improvement in Kg. However, as interactions become too severe due to increasing impeller diameter and tip speed, Kg and the mass/energy ratio decrease relative to the values for the unbaffled tank. (ii) at high impeller depths of immersion, Kg decrease markedly with a simultaneous increase in the impeller power consumption, leading to a dramatic decrease in the mass/energy ratio; Therefore, it is beneficial to remove baffles for impeller operations at high depths in an asymmetrical tank. The results also add substantial support to the findings of DeGraaf [5] that: 6. The process of gas dispersion and the consequent generation of a gas-liquid interfacial area are different from the process of fluid mixing. The optimum conditions for each process are not related. 7. The use of dimensionless correlations to predict gas dispersion and impeller power consumption is inappropriate for gas-liquid systems where the gas is introduced into the liquid through impeller gas pumping. The classical mixing power equations for impellers markedly overestimate power requirements during impeller gas dispersion. 8. Since Kg (which appears to be responsible for the interface mobility and the effective interfacial area) continues to increase despite the drop in power consumption, it is impossible to use volumetric power draw to correlate the generation of gas-liquid interfacial area or Kg. Modelling results have shown that the greatest benefit in zinc pressure leaching performance seems to be increasing the value of Kg [62,63]. However, the rate limiting 95 process in the zinc pressure leaching process is still undefined. Table I in Appendix A shows a range of high Kg values obtained in this work for various conditions shown. These values fall within the range required by leaching models, which have been estimated as 3.7 to 10 min"1 in the first stage zinc pressure leach of tank volume 32 m3. The volumetric power draw which corresponds to Kg at the top of range is similar to that of the first stage of the zinc pressure leaching when the motor is running at maximum load, i.e., 3.5 kW/m3 with 150 HP. Although air spargers were completely absent in this study, relatively high Kg values were obtained with only impeller gas pumping. This shows that impellers that are not too deep pump gas and generate many small gas bubbles thereby increasing the interfacial area and Kg. This disproves the general notion that only spargers create bubbles and impellers only mix. It was also believed that oxygen bubbles from spargers were completely consumed before they broke the surface but this has been found to be false. DeGraaf's studies revealed that only about 20 ~ 40 % of the oxygen is depleted before the bubbles break the surface [5]. It needs to be noted that those bubbles that enter the gas plenum could be recycled into the solution by the impeller agitation. The conclusions drawn from this study provide extensive opportunities for ensuring the efficacy of pressure leaching systems. They could be used as a guide to ensure optimum production rates of current pressure leach plants and effectively design new plants, where gas-liquid mass transfer is known to be rate limiting. Also, in cases where the rate limiting factor is not defined (e.g. the zinc pressure leaching process), but gas-liquid mass transfer is potentially an important requirement, the application of these findings would solve any rate limiting problem that could emanate from gas-liquid mass transfer. This is because the concepts set out in the conclusions inherently eliminate such problems. 96 5.2 Recommendations for future work 1. The flow patterns generated with an open flat turbine and their effect on gas-liquid mass transfer should be examined with and without baffles. 2. Also, the effect of flow patterns with a disc turbine should be studied in cases where the disc is (a) above and (b) below the turbine blades. The change in disc diameter and what changes this might cause in the gas-liquid mass transfer processes should be given consideration. 3. The importance of a draft tube8 in the impeller gas pumping should be examined more extensively. 4. The total effect of impeller gas pumping and other modes of gas sparging besides the conventional sparging just below the impeller should be studied. A sparger design consisting of many small diameter openings arranged in a circular form around the perimeter bottom of the tank should be considered. This kind of sparger would ensure the generation of many small gas bubbles with the intention of increasing the interfacial area. 5. An alternative means of determining the experimental critical tip speed should be directed towards the use of a variable speed motor. Depending on the impeller depth, the speed of the impeller should be varied until continuous bubbles start to form within the impeller envelope and a vortex is seen to reach the impeller blades. 8 A hollow tube within which the impeller shaft turns and maintains a constant clearance from the tube walls. This tube is expected to run from above the liquid surface to just above the turbine blades. 97 REFERENCES 1. Hiskey, B.J. and Wadsworth, E.M., "Electrochemical Processes in the Leaching of Metal Sulphides and Oxides", Process and Fundamental Considerations of Selected Hydrometallurgical Systems, Ed. Martin C. Kuhn, AIME, 1981, 303-328. 2. Peters, E., "Oxygen Utilization in Hydrometallurgy, Fundamental and Practical issues", Paper presented at symposium on the Impact of Oxygen on the Productivity of Non-Ferrous Metallurgical Processes, 1987, Annual CIM Conference of Metallurgists, Winnipeg, August 1987. 3. DeGraaf, K.B., Peters, E., and Swinkels, G.M., "An Investigation of Gas-Liquid Mass Transfer Rates in Oxygen Consuming Systems", Annual CIM Conference of Metallurgists, August, 18-21, 1985, Paper No. 44.2. 4. Biegler, T., Rand, D.A.J., and Woods, R., 1976, in Trends in Electrochemistry, Eds., Bockris, J.O.M., Rand, D.J.A., and Welsh, B.J., Plenum Press, 291-302. 5. DeGraaf, K.B., "An Investigation of Gas-Liquid Mass Transfer in Mechanically Agitated Systems", MASc Thesis, U.B.C., 1984. 6. Kuhn, M.C., Arbiter, N. and Kling, H., "Anaconda's Arbiter Process for Copper" CIM Bull., Feb., 1974, vol.67, No.742, 62-71. 7. 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Danckwerts, P.V., "Gas-Liquid Reactions", pp.232-254., McGraw-Hill, New York 1970. 14. Pierre, E.L., Francois, B., and Henri, R., "Oxidation of Cu(I) by Oxygen Gas in Concentrated NaCl Solutions", Chem. Eng. Sci., vol.36, No.9,1981, 1475-1488. 15. Calderbank, P.H., "Part I: The Interfacial Area in Gas-Liquid Contacting with Mechanical Agitation", Trans. Inst. Chem. Eng., vol.36, 1958, pp 443-458. 16. Calderbank, P.H., "Part II: Mass Transfer Coefficients in Gas-Liquid Contacting with and without Mechanical Agitation, Trans. Inst. Chem. Eng., vol.37,1959, pp 173-185 17. Sharma, M.M. and Danckwerts, P.V., Bio. Chem. Eng. 1970, vol.15, 322. 18. Shridhar, T. and Potter, O.E., "Interfacial Area Measurements in Gas-Liquid Agitated vessels", Chem. Eng. Sci., vol.33,1978,1347-1353. 19. Westerterp, K.R., Van Dierendonck, L.L., and De Kraa, J.A., "Interfacial Areas in Agitated Gas-Liquid Contactors", Chem. Eng. Sci., 1963, vol.18,157-176. 20. Preen, B.V., PhD Thesis, University of Durham, South Africa, 1961. 99 21. Holland, F.A., and Chapman, F.S., Eds., Liquid Mixing and Processing in Stirred Tanks, Lever Brothers Company, New York, N.Y.(1966) 22. Osseo-Asare, K., Introduction to Hydrometallurgy (Lecture notes), The Pennsylvania State University. 23. Oldshue, J.Y., Fluid Mixing Technology, Chemical Engineering, 1983, New York, N.Y. 24. Linek, V. and Mayrhoferova, J., Journal of Chem. Eng. Sci., 1969, vol.24, 481 25. Boema, H. and Lankester, J.H., Chem. Eng. Sci., 1968, vol.23,799. 26. Pandil, A.A. and Joshi, J.B., Chem. Eng. Sci., 1983, vol.38,1189. 27. Peters, E., Hydrometallurgy: Theory and Practice, Supplementary Notes, Dept. of Metals and Materials Eng., U.B.C. 28. Rushton, J.A., Costich, E.W.,and Everett, H.J., "Power Characteristics of Mixing Impellers", Chem. Eng. Prog., 1950, vol.46, No.8, 395. 29. Kalinske, A.A., Sewage and Indust. Wastes, 1955,27. 30. Oyama, Y. and Endoh, K., Chem. Eng., (Japan), 1955, vol.19,2. 31. Rushton, J.H. and Oldshue, J.Y., Chem. Eng. Progr., Symposium series, 1959, vol.55, 181. 32. Filler, E.C. and Crist, R.H., J. Am. Chem. Eng. Soc, 1941, vol.63, 1644. 33. Barron, C H . and O'hern, H.A., Chem. Eng. Sci., 1966, vol.21, 397. 34. Schultz, J.S. and Gaden Jr, E.L., "Sulphite Oxidation as a Measure of Aeration Effectiveness", Indust. Eng. Chem., 1956, vol.48, No. 12, 2209. 35. Linek, V. and Vacek, V., "Chemical Engineering Use of Catalysed Sulphite Oxidation Kinetics for the Determination of Mass Transfer Characteristics of Gas-Liquid Contactors", Chem. Eng. Sci., 1981, vol.36, No.ll, 1747-1768. 36. Basset, H., and Parker, W., Journ. Chem. Soc, 1951,1540. 100 37. Linek, V. and Benes, P., "Enhancement of Oxygen Absorption into Sodium Sulphite Soluions", Biotech, and BioEng., 1978, vol.XX, 687-707. 38. Backstrom, H.L.J., J. Am. Chem. Soc, 1929, vol.49, 1460 39. Mishra, G.C. and Srivastava, R.D, Chem. Eng. Sci., 1975, vol.30,1387 40. Chen, T.I. and Barron, C.H., Ind. Eng. Chem., 1972, vol. 11,466. 41. Reinders, W. and Vies, S.I., Rec. Tran. Chim. Pays-Bas., 1925, vol.44, 249. 42. Srivastava, R.D., McMillan, A.F., and Harris, I.J. "The Kinetics of Oxidation of Sodium Sulphite", Can. J. Chem. Eng., 1968, vol.46, No.6,181. 43. Dewaal, K.J.A. and Okeson, J.C, Chem. Eng. Sci., 1966, vol.21, 559. 44. Dewaal, K.J.A., Doctoral Thesis, Delft, 1965. 45. Schermerhorn, J., Master's Thesis, Laboratorium Voor Fysische Technologie, Delft, 1964. 46. Linek, V. and Mayrhoferova, J., "The Kinetics of Oxidation of Aqueous Sodium Sulphite Solutions", Chem. Eng. Sci., 1970, vol.25, 787-800. 47. Wessenlingh, J.A. and Van't Hoog, A . C , Trans. Inst. Chem. Eng., 1970,48. 48. Reith, T. and Beck, W.J., "The Oxidation of Aqueous Sodium Sulphite Solutions", Chem. Eng. Sci., 1973, vol.28,1331-1339. 49. Linek, V., Krivsky, Z., and Hudee, P., Chem. Eng. Sci., 1977, vol.32, 323 50. Linek, V. and Tvrdik, J., Biotech. Bioeng., 1971, vol.13, 53,82. 51. Callow, D.S., Gillet, W.A., and Pirt, S.J., Journ. Chem. Ind., 1957,418. 52. Reith, T., Doctoral Thesis, Tech. Univ., Delft, 1968 53. Van Dierendonck, L.L., Doctoral Thesis, Tech. Univ., Delft, 1970. 54. Linek, V., Chem. Eng. Sci., 1966, vol.21,777 55. Swiniarski, R. "Gas-Liquid Mass Transfer by Gas pumping Agitators", MASc Thesis, University of British Columbia, to be completed. 101 56. Peters, E., Private Communication, 1990, U.B.C. 57. Cumming, A. C , and Kay, S. A., A Text Book of Quantitative Chemical Analysis, Third Edition, London, 1919. 58. Bassett, J., Denney, R. C , Jeffery, G. H. and Mendham, J., Eds., Vogel's Text Book of Quantitative Inorganic Analysis, Fourth Edition, Longman, London and New York. 59. Analytical Physical Chemistry For Chemistry 201/202/205, Chemistry Department, U.B.C, 1988/1989 60. Whipple and Whipple, J. Am. Chem. Soc., 1911, 33, 362. 61. Copper, C M., Fernstrom, G. A. and Miller, S. A., Ind. Eng. Chem., 1944, 36, 504. 62. Dreisinger, D. B. and Peters, E., "The Mathematical Modelling of the Zinc Pressure Leach", The Mathematical Modelling of Metals, Ed. J. Szekely, The Metallurgical Society of AIME, 1987, pp347-369. 63. Martin, M. T. and Jankola, W. A., "Cominco's Trail Zinc Pressure leach Operation", CIM Bull, 1985,78 (876), 77-81. APPENDIX A TABLE I MASS TRANSFER PARAMETER VALUES The table below shows the highest Kg values obtained at the optimum operating conditions with the 6-bladed radial disc impellers. Depth Imp. size Tip speed ** Vol. power (cm) (cm) (m/s) (min1) (kW/m3) 11.5 23 3.47 5.3 0.48 tt tt 4.28 6.5 0.77 II 4.34 6.6 0.97 11.5 28 3.52 5.9 0.79 II II 4.53 6.1 2.62 I I II 5.28 7.8 3.47 APPENDIX B MASS TRANSFER STUDIES (Bubble movement in column) Bubble velocity Average residence time Average gas volume Liquid volume in bubble column Gas hold up a Sauter mean diameter 0.196 m/sec 4.67 sec 22.68 cm3 350 cm3 (0.35 x 10'3 m3) 0.06 = 3.51 mm or 3.51 x 10'3m Specific surface area (Interfacial area) , 6a = 1.026 cm"1 or 102.6 m"1 Concentration of sulphite C so; = 0.1 kmole/m3 Solubihty of oxygen C*0 = 1.19mole/m3 Rate of sulphite depletion -dC = 19.22 mole/m3-min Oxygen mass transfer rate R0i = 9.61 mole/m3-rriin = 5.6 x 10"5 mole/sec = 1.8 x 10"6kgO2/sec 104 Overall mass transfer parameter M,//=^r =8.08 min"1 co2 Liquid side mass transfer coefficient kt = 0.135 sec1 = 1.316 x 10"3 m/sec 105 APPENDIX C RATE OF OXYGEN MASS TRANSFER CALCULATION BASED ON COMINCO'S ZINC PRESSURE LEACH OPERATIONS Martin, M. T. and Jankola, W. A., "Cominco's Trail Zinc Pressure Leach Opertion", CIM, 78 (876)(1985), 77-81 Hayduk, W., "Solubility of Oxygen in Sulphuric Acid-Zinc Pressure Leaching Solutions", presented at Canadian Zinc Processors Assoc. meeting at Trail, B.C., April, 1990 The following reactions show the basic equations for zinc sulphide decomposition by oxidative pressure leaching, References: Peters, E., Private communication, 1991 (a) (b) ic) (ci) Operating conditions: Total pressure = 12.8 atm (1300 kPa) Temperature = 145 ~ 155 °C 106 Working volume = 100 m3 Volume of first compartment = 32 m3 Retention time = 100 min at design rate If the Cominco autoclave is treating Sullivan zinc concentrates at 51 % Zn, 9 % Fe, 5 % Pb and 30 % S, and the zinc content of the solution increases from 50 to 120 g/1 Zn, then the oxygen consumption is calculated as follows. Element % Oxidized g/1 oxidized mol/1 oxidized mol/1 oxygen Zn 100 fjx70 1.07 1.07x0.5 Fe 100 £ x 7 0 0.22 0.22x0.75 Pb 100 ^x70 0.0331 0.0331x0.5 S 2 0.02x^x70 0.0257 0.0257x1.5 0.151molesll Therefore, 0.757molesll (757moleslm3) oxygen is consumed in 100 minutes under standard conditions (at 100 % operating capacity) over all 4 compartments. In a minute the rate of oxygen consumption is 7.57 moles/m3 -minute. Cominco has run the autoclave at 200 % of standard rate and obtained 75 % of the extraction in the first compartment of 32 m3 operating volume. The resulting rate of oxygen consumption in this compartment would be given by 107 200 0.75 = 35.5 moles/m3 - minute At an average autoclave temperature of 150 °C the solubility of oxygen could be estimated from Hayduk's data as 0.64 moleslm3atm or 4.8 moleslm3 (at oxygen partial pressure of 7.5 atm). If the steady-state oxygen concentration of the slurry is zero (i.e. virtual maximum rate for oxygen absorption), then K, > f | - 7.4 min-

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